DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan
|
|
- Dorothy Harper
- 5 years ago
- Views:
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
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 informationHigher-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 informationSolution 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 informationComparison 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 informationNumerical 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 informationNumerical 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 informationA 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 informationExact 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 informationμ 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 informationResearch 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 informationwavelet 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 informationNewton 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 informationPAijpam.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 informationA 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 informationModified 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 informationMonte 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 informationSome 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 informationA 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 informationTaylor 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 informationA 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 informationFinite 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 informationPOWER 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 informationResearch 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 informationNUMERICAL 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 informationTHE 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 informationFinite 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 informationEXACT 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 informationTwo-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 informationNumerical 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 informationA 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 informationA 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 informationFind 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 informationPAijpam.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 informationA 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 informationNotes 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 informationThe 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 informationChapter 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 informationA 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 informationNumerical 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 informationSolving 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 informationApplication 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 informationThe 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 ( ) =!
.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 informationInverse 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 informationTHE 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 informationTHE 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 informationGenerating 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 informationCastiel, 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 informationSimilarity 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 informationNUMERICAL 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 informationA 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
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 informationLecture 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 informationModified 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 informationSolving 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 informationADM 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 informationMaximum 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 informationNumerical 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 informationCS321. 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 informationTime-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 informationLecture 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
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 informationSolvability 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 informationModification 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 informationx 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 informationPC5215 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 informationChapter 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 informationStability 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 informationNumerical 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 informationStreamfunction-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 informationDynamical 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 information3. 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 informationResearch 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 informationAN 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 informationNumerical 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 informationNTMSCI 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 informationCS537. 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 informationEstimation 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 informationA 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 informationFREE 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 informationarxiv: 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 informationSPECTRUM 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 informationComputation 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 informationarxiv: 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 informationPoincaré 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 informationCHAPTER 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 informationTeaching 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 informationIN 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 informationImplicit 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 informationMost 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 informationLOWER 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 informationSAMPLING 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 informationBIBECHANA 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 informationThird-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 information62. 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 informationSubject: 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 informationMULTIPLE 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 informationNEW 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 informationA 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 informationExact 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