DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan

Size: px
Start display at page:

Download "DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan"

Transcription

1 Mathematical ad Computatioal Applicatios, Vol. 9, No. 3, pp , 04 DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS Muhammad Aslam Noor, Khalida Iayat Noor ad Asif Waheed Mathematics Departmet, COMSATS Istitute of Iformatio Techology, Park Road, Islamabad, Pakista Mathematics Departmet, HITEC Uiversity, Teila Catt, Islamabad, Pakista oormaslam@hotmail.com, khalidaoor@hotmail.com, waheedasif@hotmail.com Abstract- I this paper, we use the modified decompositio method for solvig the system of third-order oliear boudary value problems associated with obstacle problems. Some eamples of system of third-order oliear boudary value problems are give. The compariso of the results obtaied by modified decompositio method with modified variatio of parameters method is also give. Results are also show graphically that demostrate the ature of the obstacles i particular problems. The results are very ecouragig idicatig the reliability ad efficiecy of the techique. Keywords- Modified decompositio method, Adomia s polyomials, system of thirdorder oliear boudary value problem.. INTROUCTION I recet years, much attetio has bee give to solve a system of third-order obstacle boudary value problems, see [-4, 5, 6, 7]. To be more precise, we cosider the followig systems of third-order oliear boudary value problems: f, u, a c, u f, u u g r, c d, f, u, d b, ad f, u u g r, a c, u f, u, c d, f, u u g r, d b, (a) (b) with boudary coditios u a, u a, u b, 3 ad cotiuity coditios of u, u ad u iterval ab,. Here rad i, i 3 are real ad fiite costats ad ab For simplicity, we will cosider f, u at iteral poits c ad d of the g is a cotiuous fuctio o,. f u. Systems (a) ad (b) arise i obstacle, cotact, uilateral ad equilibrium problems.

2 M.A. Noor, K.I. Noor ad A. Waheed 3 Most of the problems i oceaography, ecoomics, trasportatio, oliear optimizatio, ocea wave egieerig, fluid flow through porous media ad some other braches of sciece ad egieerig are modeled by these systems, see [-] ad refereces therei. Several techiques have bee used to solve system of liear thirdorder boudary value problems associated with obstacle, cotact ad uilateral problems. All the above metioed methods are proposed to solve liear system of boudary value problems associated with obstacle, cotact ad uilateral problems. Noor et al. [5] have proposed modified variatio of parameters method for solvig system of oliear obstacle boudary value problems of eve ad odd orders. Ispired ad motivated by the recet research activities i this field, we cosider the systems of oliear boudary value problems. Adomia [] developed a ovel techique kow as Adomia decompositio method for solvig boudary value problems. Further Wazwaz [3] has modified this techique kow as modified decompositio method. Modified decompositio method has bee etesively used to solve a class of problems of diversified ature. I this paper, we agai use the modified decompositio method to solve systems of thirdorder oliear obstacle boudary value problems. The modified decompositio method provides the rapidly coverget series solutio with easily computable compoets. This techique makes the solutio procedure simple while still maitaiig the higher level of accuracy. I the preset study, we implemet this techique for solvig systems of third-order oliear boudary value problems. The idea ad techique of this paper may lead to ovel applicatios of these problems i pure ad applied scieces.. MODIFIED DECOMPOSITION METHOD Cosider the followig differetial equatio: L( u) R( u) N( u) g, () where L is the highest-order derivative which is assumed to be ivertible, R is a liear differetial operator of order lesser tha L, N u represets the oliear terms ad g is the source term. Applyig the iverse operator L to both sides of () ad usig the give coditios, we obtai u f L ( Ru) L ( N u), where the fuctio f represets the terms arisig from itegratig the source term g ad by usig the give coditios. I modified decompositio method [3], the fuctio f ca be set as the sum of two partial fuctios amely f ad f ad defies the solutio u () by the series 0 u( ) u ( ), (3) where the compoets u () are usually determied recurretly by usig the relatio u f, u f L ( Ru ) L ( N u ), u f L ( Ru ) L ( N u ), k. k k k The oliear operator N (u) ca be decomposed ito a ifiite series of polyomials give by

3 3 Decompositio Method for Solvig a System of Boudary Value Problems N ( u) 0 A where A are the so-called Adomia s polyomials. These Adomia s polyomials ca be geerated for various classes of oliearities accordig to the specific algorithm developed i [3] which yields d i A, 0,,,.! N ui (4) d i NUMERICAL RESULTS, I this sectio, we apply the modified decompositio method [3] for solvig a system of third-order oliear obstacle boudary value problems. The solutios are compared with modified variatio of parameters method ad are also graphically represeted. The results are very ecouragig idicatig the reliability ad efficiecy of the techique. Eample 3.. Cosider the system of third-order oliear boudary value problems 3 u u equivalet to system (a), f u u, g, r ad ab,,, as 3!! follows: 3 u u u, for, 3!! 3 u u u u, for, (5) 3!! 3 u u u, for, 3!! with boudary coditios u u u 0,. Case :. I this case, we implemet modified decompositio method as follows 3 u u Lu u. Applyig L o both the sides, we have 3!! 3 u u u c3 c c L L u, (6)! 3!! where the operator L is defied as follows: L. ddd, ad c, c ad c3 will be determied further by usig boudary coditios ad cotiuity coditios. 000

4 M.A. Noor, K.I. Noor ad A. Waheed 33 Substitutig the decompositio series (3) for u ad the series of polyomials for oliearity (4) ito (6), we have u c3 c c L A L u, Usig the modified decompositio method [3], we have followig approimatios u c, u c3 c c c c, u c c c c c c + c c c cc c + c c..., u u Case.:. I this case, we have Lu. u Applyig 3!! the sides, we have 3 u u u c6 c5 c4 L L u, 3!! Substitutig the decompositio series for oliearity ito (7), we have followig approimatios u c, 0 5 L o both (7) u ad the series of polyomials for u c6 c4 c5 c5 c5, 0 70 u c c c c c c + c c + c c c c c5 c5 c5 c5, Case..: 3 u u. I this case, we have Lu u. Applyig L o 3!! both the sides, we have 3 u u u c9 c8 c7 L L u, (8) 3!!

5 34 Decompositio Method for Solvig a System of Boudary Value Problems Substitutig the decompositio series for oliearity ito (8), we have followig approimatios u c, 0 8 u ad the series of polyomials for u c9 c7 c8 c8 c8, u c9 c8c9 c7 c8 c c7c8 + c7c8 c c8 c8 c8 c8, By usig modified decompositio method, we have followig formula for gettig series solutio i the whole domai from the above cases uk for, k 0 u uk for, k 0 uk for. k 0 Hece, we have the followig series solutio after two iteratios

6 M.A. Noor, K.I. Noor ad A. Waheed 35 u c3 c c c3 c3 c c c c c cc c + cc c + c c c c, for, c6 c5 c4 c6 c6 c5 c5 c4 c5 c c5 + c4 c5 + c5 c5 c4 + c c5 c5 c5, for, c9 c8 c7 c9 c9 c8 c7 c8 c9 c c7c8 c8 + c7c8 c8 + c8 c c8 c8, for (9) Now we use boudary coditios ad cotiuity coditios at ad, ad we obtai system of oliear equatios. I order to solve system of oliear equatios, we use Newto s method. Hece we have the followig values of ukow costats c ,c.04437, c , c , c , c , c , c , (0) c By usig values of ukows from (0) ito (9), we have followig aalytic solutio of system of secod-order oliear boudary value problems (5)

7 36 Decompositio Method for Solvig a System of Boudary Value Problems , for, u , for, , for. Table 3. shows the compariso of the aalytic solutio of problems (5) betwee modified decompositio method (MDM) ad modified variatio of parameters method(mvpm) Sr. No MDM MVPM Error E E E E E E E E E

8 M.A. Noor, K.I. Noor ad A. Waheed 37 Figure 3. depicts the graphical represetatio of aalytical solutio of (5) by usig modified decompositio method Eample 3.. Cosider the system of third-order oliear boudary value problems 3 equivalet to system (b), f u u, g, r ab,,, as follows: ad 3 u u, for, 3 u u, for, u u 0, u. 3 u u, for, with boudary coditios Usig the procedure of Eample 3., we have the followig series solutio after two iteratios ()

9 38 Decompositio Method for Solvig a System of Boudary Value Problems c3 c c c3 c c + c c3 c cc c c c c, for, u c6 c5 c4 c5 c6 c5 c5 c4 c5, for, c9 c8 c7 c9 c8 c7 + c8 c9 c c8c7 c8 c8 c8 c8, for (5) Now we use boudary coditios ad cotiuity coditios at ad, ad we obtai system of oliear equatios. Hece we have the followig values of ukow costats by usig the Newto method. c ,c , c , c , 3 4 c , c , c , c , c (6) By usig values of ukows from (6) ito (5), we have followig aalytic solutio of system of secod-order oliear boudary value problems () , for, u , for, , for.

10 M.A. Noor, K.I. Noor ad A. Waheed 39 Table 3. represets the compariso of the aalytic solutio of problems () betwee modified decompositio method (MDM) [] ad modified variatio of parameters method (MVPM) [5] Sr. No MDM MVPM Error E E E E E E Figure 3. is a graphical represetatio of aalytical solutio of system of third-order oliear boudary value problem () by usig modified decompositio method 4. CONCLUDING REMARKS I this paper, we have used the modified decompositio method for solvig system of third-order oliear boudary value problems. We have cosidered two eamples for both the systems. The compariso of the results obtaied by this method are also give with modified variatio of parameters method. The results are also represeted graphically which demostrate the ature of the obstacle i each problem. It

11 40 Decompositio Method for Solvig a System of Boudary Value Problems is a iterestig problem to compare these methods with other methods such as variatioal iteratio methods ad its various modificatios. Acklowdegemet- The authors are grateful to Dr. S. M. Juaid Zaidi, Rector, COMSATS Istitute of Iformatio Techology, Pakista for providig ecellet research ad academic eviromets. This research is partially supported by HEC NRPU project No: 0-966/R\&D/-553, titled: Research uit of Academic Ecellece i Geometric Fuctio Theory ad Applicatios.. The authors would like to thak the referees for their valuable ad costructive commets. 6. REFERENCES. F. Gao ad C. M. Chi, Solvig third-order obstacle problems with quartic B-splies, Applied Mathematics ad Computatio 80, 70-70, A. K. Khalifa ad M. A. Noor, Quitic splies solutios of a class of cotact problems, Mathematical ad Computer Modellig 3, 5-58, S. Momai, K. Moadi ad M. A. Noor, Decompositio method for solvig system of forth-order obstacle boudary value problems, Applied Mathematics ad Computatio 75, 83-93, M. A. Noor, Variatioal iequalities i physical oceaography, i: Ocea Wave Egieerig (edit. M. Rahma), Computatioal Mechaics Publicatios, Southampto, UK, 0 6, M. A. Noor, K. I. Noor, A. Waheed ad E. A. Al-Said, Modified variatio of parameters method for solvig system of secod-order oliear boudary value problem, Iteratioal Joural of Physical Scieces 5, 46-43, M. A. Noor ad S. I. Tirmizi, Numerical methods for uilateral problems, Joural of Computatioal ad Applied Mathematics 6, , M. A. Noor ad S. I. Trimizi, Fiite differece techiques for solvig obstacle problems, Applied Mathematics Letters, 67-7, M. A. Noor, Some developmets i geeral variatioal iequalities, Applied Mathematics ad Computatio 5, 99-77, M. A. Noor ad A. K. Khalifa, A umerical approach for odd-order obstacle problems, Iteratioal Joural of Computer Mathematics 54, 09-6, M. A. Noor, K. I. Noor ad E. Al-Said, Iterative methods for solvig ocove equilibrium variatioal iequalities, Applied Mathematics & Iformatio Scieces 6(), 65-69, 0.. S. Islam, M. A. Kha, I. A. Tirmizi, ad E. H. Twizell, No-polyomial splie approach to the solutio of a system of third-order boudary-value problems, Applied Mathematics ad Computatio 68, 5-63, G. Adomai, A review of the decompositio method i applied mathematics, Joural of Mathematical Aalysis ad Applicatios 3, , A. M. Wazwaz, Approimate solutios to boudary value problems of higher-order by the modified decompositio method, Computers & Mathematics with Applicatios 40, , 000.

Some New Iterative Methods for Solving Nonlinear Equations

Some New Iterative Methods for Solving Nonlinear Equations World Applied Scieces Joural 0 (6): 870-874, 01 ISSN 1818-495 IDOSI Publicatios, 01 DOI: 10.589/idosi.wasj.01.0.06.830 Some New Iterative Methods for Solvig Noliear Equatios Muhammad Aslam Noor, Khalida

More information

Higher-order iterative methods by using Householder's method for solving certain nonlinear equations

Higher-order iterative methods by using Householder's method for solving certain nonlinear equations Math Sci Lett, No, 7- ( 7 Mathematical Sciece Letters A Iteratioal Joural http://dxdoiorg/785/msl/5 Higher-order iterative methods by usig Householder's method for solvig certai oliear equatios Waseem

More information

Solution of Differential Equation from the Transform Technique

Solution of Differential Equation from the Transform Technique Iteratioal Joural of Computatioal Sciece ad Mathematics ISSN 0974-3189 Volume 3, Number 1 (2011), pp 121-125 Iteratioal Research Publicatio House http://wwwirphousecom Solutio of Differetial Equatio from

More information

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series

More information

Numerical Solutions of Second Order Boundary Value Problems by Galerkin Residual Method on Using Legendre Polynomials

Numerical Solutions of Second Order Boundary Value Problems by Galerkin Residual Method on Using Legendre Polynomials IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 11, Issue 6 Ver. IV (Nov. - Dec. 15), PP 1-11 www.iosrjourals.org Numerical Solutios of Secod Order Boudary Value Problems

More information

Numerical Solution of the Two Point Boundary Value Problems By Using Wavelet Bases of Hermite Cubic Spline Wavelets

Numerical Solution of the Two Point Boundary Value Problems By Using Wavelet Bases of Hermite Cubic Spline Wavelets Australia Joural of Basic ad Applied Scieces, 5(): 98-5, ISSN 99-878 Numerical Solutio of the Two Poit Boudary Value Problems By Usig Wavelet Bases of Hermite Cubic Splie Wavelets Mehdi Yousefi, Hesam-Aldie

More information

A comparative study of a system of Lotka-Voltera type of PDEs through perturbation methods

A comparative study of a system of Lotka-Voltera type of PDEs through perturbation methods Computatioal Ecology ad Software, 13, 3(4): 11-15 Article A comparative study of a system of Lotka-Voltera type of PDEs through perturbatio methods H. A. Wahab 1, M. Shakil 1, T. Kha 1, S. Bhatti, M. Naeem

More information

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method Exact Solutios for a Class of Noliear Sigular Two-Poit Boudary Value Problems: The Decompositio Method Abd Elhalim Ebaid Departmet of Mathematics, Faculty of Sciece, Tabuk Uiversity, P O Box 741, Tabuki

More information

μ are complex parameters. Other

μ are complex parameters. Other A New Numerical Itegrator for the Solutio of Iitial Value Problems i Ordiary Differetial Equatios. J. Suday * ad M.R. Odekule Departmet of Mathematical Scieces, Adamawa State Uiversity, Mubi, Nigeria.

More information

Research Article A New Second-Order Iteration Method for Solving Nonlinear Equations

Research Article A New Second-Order Iteration Method for Solving Nonlinear Equations Abstract ad Applied Aalysis Volume 2013, Article ID 487062, 4 pages http://dx.doi.org/10.1155/2013/487062 Research Article A New Secod-Order Iteratio Method for Solvig Noliear Equatios Shi Mi Kag, 1 Arif

More information

wavelet collocation method for solving integro-differential equation.

wavelet collocation method for solving integro-differential equation. IOSR Joural of Egieerig (IOSRJEN) ISSN (e): 5-3, ISSN (p): 78-879 Vol. 5, Issue 3 (arch. 5), V3 PP -7 www.iosrje.org wavelet collocatio method for solvig itegro-differetial equatio. Asmaa Abdalelah Abdalrehma

More information

Newton Homotopy Solution for Nonlinear Equations Using Maple14. Abstract

Newton Homotopy Solution for Nonlinear Equations Using Maple14. Abstract Joural of Sciece ad Techology ISSN 9-860 Vol. No. December 0 Newto Homotopy Solutio for Noliear Equatios Usig Maple Nor Haim Abd. Rahma, Arsmah Ibrahim, Mohd Idris Jayes Faculty of Computer ad Mathematical

More information

PAijpam.eu ON TENSOR PRODUCT DECOMPOSITION

PAijpam.eu ON TENSOR PRODUCT DECOMPOSITION Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314

More information

A GENERALIZED CHEBYSHEV FINITE DIFFERENCE METHOD FOR HIGHER ORDER BOUNDARY VALUE PROBLEMS

A GENERALIZED CHEBYSHEV FINITE DIFFERENCE METHOD FOR HIGHER ORDER BOUNDARY VALUE PROBLEMS A GEERALIZED CHEBYSHEV FIITE DIFFERECE METHOD FOR HIGHER ORDER BOUDARY VALUE PROBLEMS Soer Aydilik Departmet of Mathematics, Faculty of Arts ad Scieces, Isik Uiversity, 34980, Istabul, Turkey Ahmet Kiris

More information

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-

More information

Monte Carlo Optimization to Solve a Two-Dimensional Inverse Heat Conduction Problem

Monte Carlo Optimization to Solve a Two-Dimensional Inverse Heat Conduction Problem Australia Joural of Basic Applied Scieces, 5(): 097-05, 0 ISSN 99-878 Mote Carlo Optimizatio to Solve a Two-Dimesioal Iverse Heat Coductio Problem M Ebrahimi Departmet of Mathematics, Karaj Brach, Islamic

More information

Some Variants of Newton's Method with Fifth-Order and Fourth-Order Convergence for Solving Nonlinear Equations

Some Variants of Newton's Method with Fifth-Order and Fourth-Order Convergence for Solving Nonlinear Equations Copyright, Darbose Iteratioal Joural o Applied Mathematics ad Computatio Volume (), pp -6, 9 http//: ijamc.darbose.com Some Variats o Newto's Method with Fith-Order ad Fourth-Order Covergece or Solvig

More information

A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation

A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation Joural of Matematics Researc; Vol No ; ISSN - E-ISSN - Publised b Caadia Ceter of Sciece ad Educatio A New Hbrid i te Noliear Part of Adomia Decompositio Metod for Iitial Value Problem of Ordiar Differetial

More information

Taylor polynomial solution of difference equation with constant coefficients via time scales calculus

Taylor polynomial solution of difference equation with constant coefficients via time scales calculus TMSCI 3, o 3, 129-135 (2015) 129 ew Treds i Mathematical Scieces http://wwwtmscicom Taylor polyomial solutio of differece equatio with costat coefficiets via time scales calculus Veysel Fuat Hatipoglu

More information

A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD

A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: 39-63 pissn: 3-7308 A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD Satish

More information

Finite Difference Approximation for Transport Equation with Shifts Arising in Neuronal Variability

Finite Difference Approximation for Transport Equation with Shifts Arising in Neuronal Variability Iteratioal Joural of Sciece ad Research (IJSR) ISSN (Olie): 39-764 Ide Copericus Value (3): 64 Impact Factor (3): 4438 Fiite Differece Approimatio for Trasport Equatio with Shifts Arisig i Neuroal Variability

More information

POWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS

POWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS Joural of Applied Mathematics ad Computatioal Mechaics 4 3(3) 3-8 POWER SERIES SOLUION OF FIRS ORDER MARIX DIFFERENIAL EQUAIONS Staisław Kukla Izabela Zamorska Istitute of Mathematics Czestochowa Uiversity

More information

Research Article Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

Research Article Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation Hidawi Iteratioal Joural of Egieerig Mathematics Volume 7, Article ID 596, 9 pages https://doi.org/.55/7/596 Research Article Laplace Trasform Collocatio Method for Solvig Hyperbolic Telegraph Equatio

More information

NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS THERMAL SCIENCE, Year 07, Vol., No. 4, pp. 595-599 595 NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS by Yula WANG *, Da TIAN, ad Zhiyua LI Departmet of Mathematics,

More information

THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES

THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES Joural of Mathematical Aalysis ISSN: 17-341, URL: http://iliriascom/ma Volume 7 Issue 4(16, Pages 13-19 THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES ABEDALLAH RABABAH, AYMAN AL

More information

Finite Difference Approximation for First- Order Hyperbolic Partial Differential Equation Arising in Neuronal Variability with Shifts

Finite Difference Approximation for First- Order Hyperbolic Partial Differential Equation Arising in Neuronal Variability with Shifts Iteratioal Joural of Scietific Egieerig ad Research (IJSER) wwwiseri ISSN (Olie): 347-3878, Impact Factor (4): 35 Fiite Differece Approimatio for First- Order Hyperbolic Partial Differetial Equatio Arisig

More information

EXACT SOLUTION OF WHITHAM-BROER-KAUP SHALLOW WATER WAVE EQUATIONS

EXACT SOLUTION OF WHITHAM-BROER-KAUP SHALLOW WATER WAVE EQUATIONS Joural of Sciece ad Arts Year 5, No. (3), pp. 5-, 5 ORIGINAL PAPER EXACT SOLUTION OF WHITHAM-BROER-KAUP SHALLOW WATER WAVE EQUATIONS JAMSHAD AHMAD, MARIYAM MUSHTAQ, NADEEM SAJJAD 3 Mauscript received:

More information

Two-step Extrapolated Newton s Method with High Efficiency Index

Two-step Extrapolated Newton s Method with High Efficiency Index Jour of Adv Research i Damical & Cotrol Systems Vol. 9 No. 017 Two-step Etrapolated Newto s Method with High Efficiecy Ide V.B. Kumar Vatti Dept. of Egieerig Mathematics Adhra Uiversity Visakhapatam Idia.

More information

Numerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative

Numerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative It. J. Adv. Appl. Math. ad Mech. () (04) 83-9 ISSN: 347-59 Available olie at www.iaamm.com Iteratioal Joural of Advaces i Applied Mathematics ad Mechaics Numerical solutio of Bagley-Torvik equatio usig

More information

A Taylor Series Based Method for Solving a Two-dimensional Second-order Equation

A Taylor Series Based Method for Solving a Two-dimensional Second-order Equation Applied Mathematical Scieces, Vol. 8, 2014, o. 66, 3255-3261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.45347 A Taylor Series Based Method for Solvig a Two-dimesioal Secod-order Equatio

More information

A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation

A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation Joural of Matematics ad Statistics 4 (: 7-, 008 ISSN 549-3644 008 Sciece Publicatios A Pseudo Splie Metods for Solvig a Iitial Value Problem of Ordiary Differetial Equatio B.S. Ogudare ad G.E. Okeca Departmet

More information

Find quadratic function which pass through the following points (0,1),(1,1),(2, 3)... 11

Find quadratic function which pass through the following points (0,1),(1,1),(2, 3)... 11 Adrew Powuk - http://www.powuk.com- Math 49 (Numerical Aalysis) Iterpolatio... 4. Polyomial iterpolatio (system of equatio)... 4.. Lier iterpolatio... 5... Fid a lie which pass through (,) (,)... 8...

More information

PAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION

PAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION Iteratioal Joural of Pure ad Applied Mathematics Volume 94 No. 204, 9-20 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v94i.2 PAijpam.eu

More information

A collocation method for singular integral equations with cosecant kernel via Semi-trigonometric interpolation

A collocation method for singular integral equations with cosecant kernel via Semi-trigonometric interpolation Iteratioal Joural of Mathematics Research. ISSN 0976-5840 Volume 9 Number 1 (017) pp. 45-51 Iteratioal Research Publicatio House http://www.irphouse.com A collocatio method for sigular itegral equatios

More information

Notes on iteration and Newton s method. Iteration

Notes on iteration and Newton s method. Iteration Notes o iteratio ad Newto s method Iteratio Iteratio meas doig somethig over ad over. I our cotet, a iteratio is a sequece of umbers, vectors, fuctios, etc. geerated by a iteratio rule of the type 1 f

More information

The Phi Power Series

The Phi Power Series The Phi Power Series I did this work i about 0 years while poderig the relatioship betwee the golde mea ad the Madelbrot set. I have fially decided to make it available from my blog at http://semresearch.wordpress.com/.

More information

Chapter 4. Fourier Series

Chapter 4. Fourier Series Chapter 4. Fourier Series At this poit we are ready to ow cosider the caoical equatios. Cosider, for eample the heat equatio u t = u, < (4.) subject to u(, ) = si, u(, t) = u(, t) =. (4.) Here,

More information

A widely used display of protein shapes is based on the coordinates of the alpha carbons - - C α

A widely used display of protein shapes is based on the coordinates of the alpha carbons - - C α Nice plottig of proteis: I A widely used display of protei shapes is based o the coordiates of the alpha carbos - - C α -s. The coordiates of the C α -s are coected by a cotiuous curve that roughly follows

More information

Numerical Conformal Mapping via a Fredholm Integral Equation using Fourier Method ABSTRACT INTRODUCTION

Numerical Conformal Mapping via a Fredholm Integral Equation using Fourier Method ABSTRACT INTRODUCTION alaysia Joural of athematical Scieces 3(1): 83-93 (9) umerical Coformal appig via a Fredholm Itegral Equatio usig Fourier ethod 1 Ali Hassa ohamed urid ad Teh Yua Yig 1, Departmet of athematics, Faculty

More information

Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods Applied ad Computatioal Mathematics 07; 6(6): 38-4 http://www.sciecepublishiggroup.com/j/acm doi: 0.648/j.acm.070606. ISSN: 38-5605 (Prit); ISSN: 38-563 (Olie) Solvig a Noliear Equatio Usig a New Two-Step

More information

Application of Homotopy Perturbation Method for the Large Angle period of Nonlinear Oscillator

Application of Homotopy Perturbation Method for the Large Angle period of Nonlinear Oscillator Applicatio of Homotopy Perturbatio Method for the Large Agle period of Noliear Oscillator Olayiwola, M. O. Gbolagade A.W., Adesaya A.O. & Akipelu F.O. Departmet of Mathematical Scieces, Faculty of Sciece,

More information

The Adomian Polynomials and the New Modified Decomposition Method for BVPs of nonlinear ODEs

The Adomian Polynomials and the New Modified Decomposition Method for BVPs of nonlinear ODEs Mathematical Computatio March 015, Volume, Issue 1, PP.1 6 The Adomia Polyomials ad the New Modified Decompositio Method for BVPs of oliear ODEs Jusheg Dua # School of Scieces, Shaghai Istitute of Techology,

More information

( a) ( ) 1 ( ) 2 ( ) ( ) 3 3 ( ) =!

( a) ( ) 1 ( ) 2 ( ) ( ) 3 3 ( ) =! .8,.9: Taylor ad Maclauri Series.8. Although we were able to fid power series represetatios for a limited group of fuctios i the previous sectio, it is ot immediately obvious whether ay give fuctio has

More information

Inverse Nodal Problems for Differential Equation on the Half-line

Inverse Nodal Problems for Differential Equation on the Half-line Australia Joural of Basic ad Applied Scieces, 3(4): 4498-4502, 2009 ISSN 1991-8178 Iverse Nodal Problems for Differetial Equatio o the Half-lie 1 2 3 A. Dabbaghia, A. Nematy ad Sh. Akbarpoor 1 Islamic

More information

THE SOLUTION OF NONLINEAR EQUATIONS f( x ) = 0.

THE SOLUTION OF NONLINEAR EQUATIONS f( x ) = 0. THE SOLUTION OF NONLINEAR EQUATIONS f( ) = 0. Noliear Equatio Solvers Bracketig. Graphical. Aalytical Ope Methods Bisectio False Positio (Regula-Falsi) Fied poit iteratio Newto Raphso Secat The root of

More information

THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT

THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT Europea Joural of Egieerig ad Techology Vol. 3 No., 5 ISSN 56-586 THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE Atif Nazir, Tahir Mahmood ad

More information

Generating Functions for Laguerre Type Polynomials. Group Theoretic method

Generating Functions for Laguerre Type Polynomials. Group Theoretic method It. Joural of Math. Aalysis, Vol. 4, 2010, o. 48, 257-266 Geeratig Fuctios for Laguerre Type Polyomials α of Two Variables L ( xy, ) by Usig Group Theoretic method Ajay K. Shula* ad Sriata K. Meher** *Departmet

More information

Castiel, Supernatural, Season 6, Episode 18

Castiel, Supernatural, Season 6, Episode 18 13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

More information

Similarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall

Similarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig

More information

NUMERICAL SOLUTIONS OF THE FRACTIONAL KdV-BURGERS-KURAMOTO EQUATION

NUMERICAL SOLUTIONS OF THE FRACTIONAL KdV-BURGERS-KURAMOTO EQUATION S5 NUMERICAL SOLUTIONS OF THE FRACTIONAL KdV-BURGERS-KURAMOTO EQUATION by Doga KAYA a*, Sema GULBAHAR a, ad Asif YOKUS b a Departmet of Matematics, Istabul Commerce Uiversity, Uskudar, Istabul, Turkey

More information

A New Solution Method for the Finite-Horizon Discrete-Time EOQ Problem

A New Solution Method for the Finite-Horizon Discrete-Time EOQ Problem This is the Pre-Published Versio. A New Solutio Method for the Fiite-Horizo Discrete-Time EOQ Problem Chug-Lu Li Departmet of Logistics The Hog Kog Polytechic Uiversity Hug Hom, Kowloo, Hog Kog Phoe: +852-2766-7410

More information

( x) SUMMARY (2) α z. (3) Now approximating z derivative by forward difference

( x) SUMMARY (2) α z. (3) Now approximating z derivative by forward difference Depth etrapolatio of seismic wavefields usig cubic splie approimatio Suhas Phadke* ad Dheera Bhardwa Cetre for Developmet of Advaced Computig, Pue Uiversity Campus, GaeshKhid, Pue 4007, Idia SUMMARY Depth

More information

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would

More information

Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis

Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis America Joural of Mathematics ad Statistics 01, (4): 95-100 DOI: 10.593/j.ajms.01004.05 Modified Ratio s Usig Kow Media ad Co-Efficet of Kurtosis J.Subramai *, G.Kumarapadiya Departmet of Statistics, Podicherry

More information

Solving third order boundary value problem with fifth order block method

Solving third order boundary value problem with fifth order block method Matematical Metods i Egieerig ad Ecoomics Solvig tird order boudary value problem wit it order bloc metod A. S. Abdulla, Z. A. Majid, ad N. Seu Abstract We develop a it order two poit bloc metod or te

More information

ADM Solution of Flow Field and Convective Heat Transfer over a Parallel Flat Plate and Comparison with the Forth Order Runge Kutta Method

ADM Solution of Flow Field and Convective Heat Transfer over a Parallel Flat Plate and Comparison with the Forth Order Runge Kutta Method Australia Joural of Basic ad Applied Scieces, 5(: -8, ISSN 99-878 ADM Solutio of Flow Field ad Covective Heat Trasfer over a Parallel Flat Plate ad Compariso with the Forth Order Ruge Kutta Method Arma

More information

Maximum likelihood estimation from record-breaking data for the generalized Pareto distribution

Maximum likelihood estimation from record-breaking data for the generalized Pareto distribution METRON - Iteratioal Joural of Statistics 004, vol. LXII,. 3, pp. 377-389 NAGI S. ABD-EL-HAKIM KHALAF S. SULTAN Maximum likelihood estimatio from record-breakig data for the geeralized Pareto distributio

More information

Numerical Method for Blasius Equation on an infinite Interval

Numerical Method for Blasius Equation on an infinite Interval Numerical Method for Blasius Equatio o a ifiite Iterval Alexader I. Zadori Omsk departmet of Sobolev Mathematics Istitute of Siberia Brach of Russia Academy of Scieces, Russia zadori@iitam.omsk.et.ru 1

More information

CS321. Numerical Analysis and Computing

CS321. Numerical Analysis and Computing CS Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 September 8 5 What is the Root May physical system ca

More information

Time-Domain Representations of LTI Systems

Time-Domain Representations of LTI Systems 2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable

More information

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would

More information

-ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION

-ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION NEW NEWTON-TYPE METHOD WITH k -ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION R. Thukral Padé Research Cetre, 39 Deaswood Hill, Leeds West Yorkshire, LS7 JS, ENGLAND ABSTRACT The objective

More information

Solvability of Multivalued General Mixed Variational Inequalities

Solvability of Multivalued General Mixed Variational Inequalities Joural of Mathematical Aalysis ad Applicatios 261, 390 402 2001 doi:10.1006 jmaa.2001.7533, available olie at http: www.idealibrary.com o Solvability of Multivalued Geeral Mixed Variatioal Iequalities

More information

Modification of Weerakoon-Fernando s Method with Fourth-Order of Convergence for Solving Nonlinear Equation

Modification of Weerakoon-Fernando s Method with Fourth-Order of Convergence for Solving Nonlinear Equation ISSN: 50-08 Iteratioal Joural o AdvacedResearch i Sciece, Egieerig ad Techology Vol. 5, Issue 8, August 018 Modiicatio o Weerakoo-Ferado s Method with Fourth-Order o Covergece or Solvig Noliear Equatio

More information

x x x Using a second Taylor polynomial with remainder, find the best constant C so that for x 0,

x x x Using a second Taylor polynomial with remainder, find the best constant C so that for x 0, Math Activity 9( Due with Fial Eam) Usig first ad secod Taylor polyomials with remaider, show that for, 8 Usig a secod Taylor polyomial with remaider, fid the best costat C so that for, C 9 The th Derivative

More information

PC5215 Numerical Recipes with Applications - Review Problems

PC5215 Numerical Recipes with Applications - Review Problems PC55 Numerical Recipes with Applicatios - Review Problems Give the IEEE 754 sigle precisio bit patter (biary or he format) of the followig umbers: 0 0 05 00 0 00 Note that it has 8 bits for the epoet,

More information

Chapter 2 The Solution of Numerical Algebraic and Transcendental Equations

Chapter 2 The Solution of Numerical Algebraic and Transcendental Equations Chapter The Solutio of Numerical Algebraic ad Trascedetal Equatios Itroductio I this chapter we shall discuss some umerical methods for solvig algebraic ad trascedetal equatios. The equatio f( is said

More information

Stability Analysis of the Euler Discretization for SIR Epidemic Model

Stability Analysis of the Euler Discretization for SIR Epidemic Model Stability Aalysis of the Euler Discretizatio for SIR Epidemic Model Agus Suryato Departmet of Mathematics, Faculty of Scieces, Brawijaya Uiversity, Jl Vetera Malag 6545 Idoesia Abstract I this paper we

More information

Numerical Methods in Fourier Series Applications

Numerical Methods in Fourier Series Applications Numerical Methods i Fourier Series Applicatios Recall that the basic relatios i usig the Trigoometric Fourier Series represetatio were give by f ( x) a o ( a x cos b x si ) () where the Fourier coefficiets

More information

Streamfunction-Vorticity Formulation

Streamfunction-Vorticity Formulation Streamfuctio-Vorticity Formulatio A. Salih Departmet of Aerospace Egieerig Idia Istitute of Space Sciece ad Techology, Thiruvaathapuram March 2013 The streamfuctio-vorticity formulatio was amog the first

More information

Dynamical stability and parametrical vibrations of the laminated plates with complex shape

Dynamical stability and parametrical vibrations of the laminated plates with complex shape (3) 75 88 Dyamical stability ad parametrical vibratios of the lamiated plates with comple shape Abstract The problem of oliear vibratios ad stability aalysis for the symmetric lamiated plates with comple

More information

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense, 3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [

More information

Research Article Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial

Research Article Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial Mathematical Problems i Egieerig Volume 24, Article ID 43965, 5 pages http://dx.doi.org/.55/24/43965 Research Article Numerical Solutio of Fractioal Itegro-Differetial Equatios by Least Squares Method

More information

AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC MAPS

AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC MAPS http://www.paper.edu.c Iteratioal Joural of Bifurcatio ad Chaos, Vol. 1, No. 5 () 119 15 c World Scietific Publishig Compay AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC

More information

Numerical Solution of Fredholm Integral Equations Using Hosoya Polynomial of Path Graphs

Numerical Solution of Fredholm Integral Equations Using Hosoya Polynomial of Path Graphs America Joural of Numerical Aalysis, 7, Vol. 5, No., -5 Available olie at http://pubs.sciepub.com/aja/5// Sciece ad Educatio Publishig DOI:.69/aja-5-- Numerical Solutio of Fredholm Itegral Equatios Usig

More information

NTMSCI 5, No. 1, (2017) 26

NTMSCI 5, No. 1, (2017) 26 NTMSCI 5, No. 1, - (17) New Treds i Mathematical Scieces http://dx.doi.org/1.85/tmsci.17.1 The geeralized successive approximatio ad Padé approximats method for solvig a elasticity problem of based o the

More information

CS537. Numerical Analysis and Computing

CS537. Numerical Analysis and Computing CS57 Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 Jauary 9 9 What is the Root May physical system ca be

More information

Estimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable

Estimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable Iteratioal Joural of Probability ad Statistics 01, 1(4: 111-118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig Co-Efficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya

More information

A GENERALIZATION OF THE SYMMETRY BETWEEN COMPLETE AND ELEMENTARY SYMMETRIC FUNCTIONS. Mircea Merca

A GENERALIZATION OF THE SYMMETRY BETWEEN COMPLETE AND ELEMENTARY SYMMETRIC FUNCTIONS. Mircea Merca Idia J Pure Appl Math 45): 75-89 February 204 c Idia Natioal Sciece Academy A GENERALIZATION OF THE SYMMETRY BETWEEN COMPLETE AND ELEMENTARY SYMMETRIC FUNCTIONS Mircea Merca Departmet of Mathematics Uiversity

More information

FREE VIBRATIONS OF SIMPLY SUPPORTED BEAMS USING FOURIER SERIES

FREE VIBRATIONS OF SIMPLY SUPPORTED BEAMS USING FOURIER SERIES Abdullah : FREE VIBRATIONS OF SIMPY SUPPORTED BEAMS FREE VIBRATIONS OF SIMPY SUPPORTED BEAMS USING FOURIER SERIES SAWA MUBARAK ABDUAH Assistat ecturer Uiversity of Mosul Abstract Fourier series will be

More information

arxiv: v2 [math.fa] 21 Feb 2018

arxiv: v2 [math.fa] 21 Feb 2018 arxiv:1802.02726v2 [math.fa] 21 Feb 2018 SOME COUNTEREXAMPLES ON RECENT ALGORITHMS CONSTRUCTED BY THE INVERSE STRONGLY MONOTONE AND THE RELAXED (u, v)-cocoercive MAPPINGS E. SOORI Abstract. I this short

More information

SPECTRUM OF THE DIRECT SUM OF OPERATORS

SPECTRUM OF THE DIRECT SUM OF OPERATORS Electroic Joural of Differetial Equatios, Vol. 202 (202), No. 20, pp. 8. ISSN: 072-669. URL: http://ejde.math.txstate.edu or http://ejde.math.ut.edu ftp ejde.math.txstate.edu SPECTRUM OF THE DIRECT SUM

More information

Computation of Error Bounds for P-matrix Linear Complementarity Problems

Computation of Error Bounds for P-matrix Linear Complementarity Problems Mathematical Programmig mauscript No. (will be iserted by the editor) Xiaoju Che Shuhuag Xiag Computatio of Error Bouds for P-matrix Liear Complemetarity Problems Received: date / Accepted: date Abstract

More information

arxiv: v1 [cs.sc] 2 Jan 2018

arxiv: v1 [cs.sc] 2 Jan 2018 Computig the Iverse Melli Trasform of Holoomic Sequeces usig Kovacic s Algorithm arxiv:8.9v [cs.sc] 2 Ja 28 Research Istitute for Symbolic Computatio RISC) Johaes Kepler Uiversity Liz, Alteberger Straße

More information

Poincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains

Poincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains Advaces i Pure Mathematics 23 3 72-77 http://dxdoiorg/4236/apm233a24 Published Olie Jauary 23 (http://wwwscirporg/oural/apm) Poicaré Problem for Noliear Elliptic Equatios of Secod Order i Ubouded Domais

More information

CHAPTER 10 INFINITE SEQUENCES AND SERIES

CHAPTER 10 INFINITE SEQUENCES AND SERIES CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece

More information

Teaching Mathematics Concepts via Computer Algebra Systems

Teaching Mathematics Concepts via Computer Algebra Systems Iteratioal Joural of Mathematics ad Statistics Ivetio (IJMSI) E-ISSN: 4767 P-ISSN: - 4759 Volume 4 Issue 7 September. 6 PP-- Teachig Mathematics Cocepts via Computer Algebra Systems Osama Ajami Rashaw,

More information

IN many scientific and engineering applications, one often

IN many scientific and engineering applications, one often INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS, VOL 3, NO, FEBRUARY 07 5 Secod Degree Refiemet Jacobi Iteratio Method for Solvig System of Liear Equatio Tesfaye Kebede Abstract Several

More information

Implicit function theorem

Implicit function theorem Jovo Jaric Implicit fuctio theorem The reader kows that the equatio of a curve i the x - plae ca be expressed F x, =., this does ot ecessaril represet a fuctio. Take, for example F x, = 2x x =. (1 either

More information

Most text will write ordinary derivatives using either Leibniz notation 2 3. y + 5y= e and y y. xx tt t

Most text will write ordinary derivatives using either Leibniz notation 2 3. y + 5y= e and y y. xx tt t Itroductio to Differetial Equatios Defiitios ad Termiolog Differetial Equatio: A equatio cotaiig the derivatives of oe or more depedet variables, with respect to oe or more idepedet variables, is said

More information

LOWER BOUNDS FOR THE BLOW-UP TIME OF NONLINEAR PARABOLIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS

LOWER BOUNDS FOR THE BLOW-UP TIME OF NONLINEAR PARABOLIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS Electroic Joural of Differetial Equatios, Vol. 214 214), No. 113, pp. 1 5. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.ut.edu ftp ejde.math.txstate.edu LOWER BOUNDS FOR THE BLOW-UP

More information

SAMPLING LIPSCHITZ CONTINUOUS DENSITIES. 1. Introduction

SAMPLING LIPSCHITZ CONTINUOUS DENSITIES. 1. Introduction SAMPLING LIPSCHITZ CONTINUOUS DENSITIES OLIVIER BINETTE Abstract. A simple ad efficiet algorithm for geeratig radom variates from the class of Lipschitz cotiuous desities is described. A MatLab implemetatio

More information

BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics

BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics Mohd Yusuf Yasi / BIBECHANA 8 (2012) 31-36 : BMHSS, p. 31 BIBECHANA A Multidiscipliary Joural of Sciece, Techology ad Mathematics ISSN 2091-0762 (olie) Joural homepage: http://epjol.ifo/ide.php/bibechana

More information

Third-order Composite Runge Kutta Method for Solving Fuzzy Differential Equations

Third-order Composite Runge Kutta Method for Solving Fuzzy Differential Equations Global Joural of Pure ad Applied Mathematics. ISSN 097-768 Volume Number (06) pp. 7-76 Research Idia Publicatios http://www.ripublicatio.com/gjpam.htm Third-order Composite Ruge Kutta Method for Solvig

More information

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + 62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of

More information

Subject: Differential Equations & Mathematical Modeling -III. Lesson: Power series solutions of Differential Equations. about ordinary points

Subject: Differential Equations & Mathematical Modeling -III. Lesson: Power series solutions of Differential Equations. about ordinary points Power series solutio of Differetial equatios about ordiary poits Subject: Differetial Equatios & Mathematical Modelig -III Lesso: Power series solutios of Differetial Equatios about ordiary poits Lesso

More information

MULTIPLE TIME SCALES SOLUTION OF AN EQUATION WITH QUADRATIC AND CUBIC NONLINEARITIES HAVING FRAC- TIONAL-ORDER DERIVATIVE

MULTIPLE TIME SCALES SOLUTION OF AN EQUATION WITH QUADRATIC AND CUBIC NONLINEARITIES HAVING FRAC- TIONAL-ORDER DERIVATIVE Mathematical ad Computatioal Applicatios, Vol. 6, No., pp. 3-38,. Associatio for Scietific Research MULIPLE IME SCALES SOLUION OF AN EQUAION WIH QUADRAIC AND CUBIC NONLINEARIIES HAVING FRAC- IONAL-ORDER

More information

NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS

NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS Joural of Applied Aalysis ad Computatio Volume 5, Number 2, May 25, 22 23 Website:http://jaac-olie.com/ doi:.948/252 NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS Jie Su,2, Wei Qiao

More information

A Parametric Approach to Solve Bounded-Variable LFP by Converting into LP

A Parametric Approach to Solve Bounded-Variable LFP by Converting into LP Iteratioal Joural of Operatios Research Iteratioal Joural of Operatios Research Vol., No., 0707 (06 A Parametric Approach to Solve ouded-variable LFP by Covertig ito LP Saal Chakroborty ad M. abul Hasa

More information

Exact Solutions of the Generalized Benjamin Equation and (3 + 1)- Dimensional Gkp Equation by the Extended Tanh Method

Exact Solutions of the Generalized Benjamin Equation and (3 + 1)- Dimensional Gkp Equation by the Extended Tanh Method Available at http://pvamuedu/aam Appl Appl Math ISSN: 93-9466 Vol 7, Issue (Jue 0), pp 75 87 Applicatios ad Applied Mathematics: A Iteratioal Joural (AAM) Exact Solutios of the Geeralized Bejami Equatio

More information