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

Size: px
Start display at page:

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

Transcription

1 IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: pissn: A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD Satish V Desale, V H Pradha R.C.Patel Istitute of Techology, Shirpur, Idia satishdesale@gmail.com S.V.Natioal Istitute of Techology, Surat, Idia pradha65@yahoo.com Abstract The problem of the MHD boudary layer flow of a icompressible viscous fluid over a o-liear stretchig sheet is discussed. Usig similarity trasformatio goverig equatios are trasformed i to oliear ordiary differetial equatio. The Implicit fiite differece Keller box method is applied to fid the umerical solutio of oliear differetial equatio. Graphical results of fluid velocity have bee preseted ad discussed for the related parameters. Keywords: MHD, boudary layer, oliear differetial equatios, ad Keller box method *** INTRODUCTION I 973, McCormack & Crae [8] itroduced the stretchig sheet problem. The stretchig problems for steady flow have bee used i various egieerig ad idustrial processes, like o-newtoia fluids, MHD flows, porous plate, porous medium ad heat trasfer aalysis. Magetohydrodyamics (MHD) is the study of the iteractio of coductig fluids with electromagetic pheomea. The flow of a electrically coductig fluid i the presece of a magetic field is importat i various areas of techology ad egieerig such as MHD power geeratio, MHD flow meters, MHD pumps, etc. Chiam [7] ivestigated the MHD flow of a viscous fluid bouded by a stretchig surface with power law velocity. He obtaied the umerical solutio of the boudary value problem by usig the Ruge Kutta shootig algorithm with Newto iteratio. Hayat et al. [6] applied the modified Adomia decompositio method with the Padé approximatio ad obtaied the series solutio of the goverig oliear problem. Rashidi i [4] used the differetial trasform method with the Padé approximat ad developed aalytical solutios for this problem. I [, ] applied the HAM i order to obtai a aalytical solutio of the goverig oliear differetial equatios.. GOVERNING EQUATIONS Cosider the Magetohydrodyamic flow of a icompressible viscous fluid over a stretchig sheet at y = 0. The fluid is electrically coductig uder the ifluece of a applied magetic field B(x) ormal to the stretchig sheet. The iduced magetic field is eglected. The resultig boudary layer equatios are as follows [6] u v + = 0 x y u v u B ( x) u + v = ν σ u x y y ρ where u ad v are the velocity compoets i the x - ad y directios respectively, ν is the kiematic viscosity, ρ is the fluid desity ad σ is the electrical coductivity of the fluid. I equatio (), the exteral electric field ad the polarizatio effects are egligible ad followig Chiam [7] we assume that the magetic field B takes the form B ( )/ ( x) = B x The boudary coditios correspodig to the o-liear stretchig of the sheet are [6] 0 () () I this paper, MHD boudary layer equatio is solved with the u( x,0) = cx, v( x,0) = 0 help of implicit fiite differece Keller box method ad various results are discussed graphically. Volume: 0 Issue: Dec-03, 87

2 IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: pissn: u( x, y) 0, y where c ad are costats. usig the followig substitutios c( + ) t = x y v Now, write the fiite differece approximatios of the ordiary differetial equatios (5)-(6) for the midpoit x, t of the segmet usig cetered differece x, t derivatives, this is called ceterig about. u = cx f ( t) c( + ) v = x f ( t) t f ( t) v + + Equatio ()-() are trasformed to f f u = h u u v + v = h (9) (0) ( ) ( ) + ( ) ( ) β ( ) ( ) = 0 f t f t f t f t Mf t with the followig boudary coditios f f f (0) = 0, (0) =, ( ) = 0 σ B0 β =, M = Where + ρc( + ). 3. KELLER BOX METHOD Equatio (3) subect to the boudary coditios (4) is solved umerically usig implicit fiite differece method that is kow as Keller-box i combiatio with the Newto s liearizatio techiques as described by Cebeci ad Bradshaw [3]. This method is ucoditioally stable ad has secodorder accuracy. I this method the trasformed differetial equatio (3) are writes i terms of first order system, for that itroduce ew depedet variable u, v such that f = u u = v Where prime deotes differetiatio with t. + β = 0 v fv u Mu with the ew boudary coditios (4) (3) (5) (6) (7) Now, ordiary differetial equatio (7) is approximated by the x ceterig about the mid-poit, t of the rectagle. x, t I first step we ceter about without specifyig t. ( v ) + ( fv ) β ( u ) Mu ( ) ( ) β ( ) = v + fv u Mu Now ceterig about (for simplicity, remove ) v v f + f v + v + h u u u β M = v v ( fv) β ( u ) Mu / + / h / () Now liearize the oliear system of equatios (9)-() usig the Newto s quasi-liearizatio method [5] For that use, f (0) = 0, u(0) =, u( ) = 0 (8) Volume: 0 Issue: Dec-03, 88

3 IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: pissn: f = f + δ f + u = u + δu + v = v + δ v + Equatio (8) to(0) ca be rewritte as h f f ( u ) = ( r ) () δ δ δ δ h u u ( v + v ) = ( r ) (3) δ δ δ δ This block tridiagoal structure ca be solved usig LU method explaied by Na [5]. 4. RESULT AND DISCUSSION Graphically, effects of magetic parameter ad odimesioal parameter β o velocity profile are show i followig figures. Fig. ad shows, as the magetic parameter M ad o-dimesioal parameter β icreases, the fluid velocity decreases. Also it ca be observed that as magetic parameter M icreases velocity profile decreases very rapidly as compared to icrease of o-dimesioal parameter β. Fig 3 ad 4 shows the effect of magetic parameter o f. ( a ) δv + ( a ) δv + ( a ) δ f + ( a ) δ f ( ) ( a ) δu + ( a ) δu = r (4) The liearized differece system of equatios ()-(4) has a block tridiagoal structure. I a vector matrix form, it ca be writte as [ ] [ ] A C [ ] [ ] [ ] B A C [ ] [ ] [ ] [ ] [ ] [ δ ] [ r ] [ δ ] [ r ] [ δ ] [ r ] 3 3 B A C : : : = : [ B ] [ A ] [ C ] : : B A [ δ ] [ r ] Fig -:.Effect of Magetic Parameter o fluid velocity obtaied by Keller Box Method for β = Volume: 0 Issue: Dec-03, 89

4 IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: pissn: Fig -: Effect of o fluid velocity obtaied by Keller Box Method whe M = Fig -3: Effect of Magetic Parameter o f (t) obtaied by Keller Box Method for β = Fig -4: Effect of Magetic Parameter o f (t) obtaied by Keller Box Method for β = Volume: 0 Issue: Dec-03, 90

5 IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: pissn: CONCLUSIONS I this study, MHD viscous flow over a stretchig sheet is cosidered. Keller Box Method is applied to solve the goverig oliear differetial equatio. The results idicate that the velocity will be reduced by icreasig the two parameters of M ad β; however, effect of M i reductio of the velocity compoets is more tha β. Therefore, it ca be cocluded that Keller Box is oe of the best method to study o MHD viscous flow umerically ad get the appropriate results. REFERENCES [] A.Mehmood, S. Muawar, A. Ali, Commets to: Homotopy aalysis method for solvig the MHD flow over a o-liear stretchig sheet (Commu. Noliear Sci. Numer. Simulat. 4 (009) ), Commuicatios i Noliear Sciece ad Numerical Simulatio, 5 (00) [] A.R. Ghotbi, Homotopy aalysis method for solvig the MHD flow over a o-liear stretchig sheet, Commuicatios i Noliear Sciece ad Numerical Simulatio,4 (009) [3] Cebeci T., Bradshaw P. Physical ad computatioal Aspects of Covective Heat Trasfer, New York: Spriger (988), [4] M.M. Rashidi, The modified differetial trasform method for solvig MHD boudary-layer equatios, Computer Physics Commuicatio, 80 (009), 0-7. [5] Na T.Y., Computatioal Methods i Egieerig Boudary Value Problem. New York: Academic Press (979), -8. [6] T. Hayat, Q. Hussai, T. aved, The modified decompositio method ad Padé approximats for the MHD flow over a o-liear stretchig sheet, Noliear Aalysis: Real World Applicatios, 0 (009), [7] T.C. Chiam, Hydromagetic flow over a surface stretchig with a power-law velocity, It.. Eg. Sci. 33 (995), [8] McCormack P.D., Crae L., "Physics of Fluid Dyamics", New York, Academic Press, (973). Volume: 0 Issue: Dec-03, 9

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

Boundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary

Boundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary Boudary layer problem o coveyor belt Gabriella Bogár Uiversity of Miskolc 355 Miskolc-Egyetemváros, Hugary e-mail: matvbg@ui-miskolc.hu Abstract: A techologically importat source of the boudary layer pheomeo

More information

Numerical Study on MHD Flow And Heat Transfer With The Effect Of Microrotational Parameter In The Porous Medium

Numerical Study on MHD Flow And Heat Transfer With The Effect Of Microrotational Parameter In The Porous Medium IOSR Joural of Egieerig (IOSRJEN) ISSN (e): 5-3, ISSN (p): 78-879 Vol. 5, Issue 4 (April. 5), V PP 8-7 www.iosrje.org Numerical Study o MHD Flow Ad Heat rasfer With he Effect Of Microrotatioal Parameter

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

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

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

DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan Mathematical ad Computatioal Applicatios, Vol. 9, No. 3, pp. 30-40, 04 DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS Muhammad Aslam Noor, Khalida Iayat Noor ad Asif Waheed

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

Unsteady Natural Convective Flow over an Impulsively Started Semi-Infinite Vertical Plate in the Presence of Porous Medium with Chemical Reaction

Unsteady Natural Convective Flow over an Impulsively Started Semi-Infinite Vertical Plate in the Presence of Porous Medium with Chemical Reaction Joural of Applied Fluid Mechaics, Vol. 9, No., pp. 95-0, 06. Available olie at www.jafmolie.et, ISSN 735-357, EISSN 735-3645. Usteady Natural Covective Flow over a Impulsively Started Semi-Ifiite Vertical

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

FUZZY ALTERNATING DIRECTION IMPLICIT METHOD FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS

FUZZY ALTERNATING DIRECTION IMPLICIT METHOD FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS FUZZY ALTERNATING DIRECTION IMPLICIT METHOD FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS N.Mugutha *1, B.Jessaili Jeba #2 *1 Assistat Professor, Departmet of Mathematics, M.V.Muthiah

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

Effect of Melting and Thermo-Diffusion on Natural Convection Heat Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

Effect of Melting and Thermo-Diffusion on Natural Convection Heat Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium The Ope Trasport Pheomea Joural, 29,, 7-4 7 Ope Access Effect of Meltig ad Thermo-Diffusio o Natural Covectio Heat Mass Trasfer i a No-Newtoia Fluid Saturated No-Darcy Porous Medium R.R. Kairi ad P.V.S.N.

More information

THE ANALYSIS OF A REACTIVE HYDROMAGNETIC FLUID FLOW IN A CHANNEL THROUGH A POROUS MEDIUM WITH CONVECTIVE COOLING

THE ANALYSIS OF A REACTIVE HYDROMAGNETIC FLUID FLOW IN A CHANNEL THROUGH A POROUS MEDIUM WITH CONVECTIVE COOLING U.P.B. Sci. Bull., Series D, Vol. 78, Iss. 4, 16 ISSN 1454-358 HE ANALYSIS OF A REACIVE HYDROMAGNEIC FLUID FLOW IN A CHANNEL HROUGH A POROUS MEDIUM WIH CONVECIVE COOLING Athoy Rotimi HASSAN 1 * ad Riette

More information

Magnetic Effect on Free Convection in a Non-Darcy Porous Medium Saturated with Doubly Stratified Power-Law Fluid

Magnetic Effect on Free Convection in a Non-Darcy Porous Medium Saturated with Doubly Stratified Power-Law Fluid D. Sriivasacharya dsc@itw.ac.i dsriivasacharya@yahoo.com Magetic Effect o Free ovectio i a No-Darcy Porous Medium Saturated with Doubly Stratified Power-Law Fluid J. Praitha Natural covectio heat ad mass

More information

A numerical Technique Finite Volume Method for Solving Diffusion 2D Problem

A numerical Technique Finite Volume Method for Solving Diffusion 2D Problem The Iteratioal Joural Of Egieerig d Sciece (IJES) Volume 4 Issue 10 Pages PP -35-41 2015 ISSN (e): 2319 1813 ISSN (p): 2319 1805 umerical Techique Fiite Volume Method for Solvig Diffusio 2D Problem 1 Mohammed

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

EFFECTS OF THERMAL STRATIFICATION ON FLOW AND HEAT TRANSFER DUE TO A STRETCHING CYLINDER WITH UNIFORM SUCTION/INJECTION

EFFECTS OF THERMAL STRATIFICATION ON FLOW AND HEAT TRANSFER DUE TO A STRETCHING CYLINDER WITH UNIFORM SUCTION/INJECTION Iteratioal Joural of Eergy & Techology ISSN 035-911X www.joural-eertech.eu Iteratioal Joural of Eergy & Techology (4) (010) 1 7 EFFECTS OF THERMAL STRATIFICATION ON FLO AND HEAT TRANSFER DUE TO A STRETCHING

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

1. Linearization of a nonlinear system given in the form of a system of ordinary differential equations

1. Linearization of a nonlinear system given in the form of a system of ordinary differential equations . Liearizatio of a oliear system give i the form of a system of ordiary differetial equatios We ow show how to determie a liear model which approximates the behavior of a time-ivariat oliear system i a

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

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

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

HALF-SWEEP GAUSS-SEIDEL ITERATION APPLIED TO TIME-FRACTIONAL DIFFUSION EQUATIONS

HALF-SWEEP GAUSS-SEIDEL ITERATION APPLIED TO TIME-FRACTIONAL DIFFUSION EQUATIONS Jural Karya Asli Loreka Ahli Matematik Vol. 8 No. () Page 06-0 Jural Karya Asli Loreka Ahli Matematik HALF-SWEEP GAUSS-SEIDEL ITERATION APPLIED TO TIME-FRACTIONAL DIFFUSION EQUATIONS A. Suarto J. Sulaima

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

CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS

CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS C.PRAX ad H.SADAT Laboratoire d'etudes Thermiques,URA CNRS 403 40, Aveue du Recteur Pieau 86022 Poitiers Cedex,

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

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

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

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

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

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

Free convection over a non-isothermal axisymmetric body immersed in a porous medium saturated with an electrically conducting non-newtonian fluid

Free convection over a non-isothermal axisymmetric body immersed in a porous medium saturated with an electrically conducting non-newtonian fluid Free covectio over a o-isothermal aisymmetric body immersed i a porous medium saturated ith a electrically coductig o-netoia fluid Abstract Shobha Bagai, Chadrashekhar Nishad Departmet of Mathematics Uiversity

More information

HOMOTOPY PERTURBATION METHOD FOR VISCOUS HEATING IN PLANE COUETTE FLOW

HOMOTOPY PERTURBATION METHOD FOR VISCOUS HEATING IN PLANE COUETTE FLOW Yu, Y.-S. et al.: Homotopy Perturbatio Method for Viscous Heatig THERMAL SCIENCE, Year 13, Vol. 17, No. 5, pp. 1355-136 1355 HOMOTOPY PERTURBATION METHOD FOR VISCOUS HEATING IN PLANE COUETTE FLOW by Yi-Sha

More information

Second Law Analysis of Ion Slip Effect on MHD Couple Stress Fluid

Second Law Analysis of Ion Slip Effect on MHD Couple Stress Fluid ITERATIOAL JOURAL OF MECHAICS Volume, 8 Secod Law Aalysis of Io Slip Effect o MHD Couple Stress Fluid Abiodu A. Opauga, Hilary I. Okagbue, Olasumbo O. Agboola, Sheila A. Bishop Abstract This paper is cocered

More information

THE FRACTAL TECHNIQUES APPLIED IN NUMERICAL ITERATIVE METHODS FRAME

THE FRACTAL TECHNIQUES APPLIED IN NUMERICAL ITERATIVE METHODS FRAME 6 th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE THE FRACTAL TECHNIQUES APPLIED IN NUMERICAL ITERATIVE METHODS FRAME George MAHALU, Radu PENTIUC Uiversity of Suceava - mahalu@eed.usv.ro Abstract: May methods

More information

Application of Homotopy Analysis Method for Solving various types of Problems of Ordinary Differential Equations

Application of Homotopy Analysis Method for Solving various types of Problems of Ordinary Differential Equations Iteratioal Joural o Recet ad Iovatio Treds i Coputig ad Couicatio IN: 31-8169 Volue: 5 Issue: 5 16 Applicatio of Hootopy Aalysis Meod for olvig various types of Probles of Ordiary Differetial Equatios

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

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

Numerical solutions for unsteady flow past a semi-infinite inclined plate with temperature oscillations

Numerical solutions for unsteady flow past a semi-infinite inclined plate with temperature oscillations Joural of Mechaical Sciece ad Techology 3 (009) 1710~1717 Joural of Mechaical Sciece ad Techology www.sprigerlik.com/cotet/1738-494x DOI 10.1007/s106-009-0415-3 Numerical solutios for usteady flow past

More information

Variational Approach of Marangoni Mixed Convection Boundary Layer Flow with Pade Technique

Variational Approach of Marangoni Mixed Convection Boundary Layer Flow with Pade Technique Joural of Applied Fluid Mechaics, Vol. 9, No. 6, pp. 949-9, 6. Available olie at www.jafmolie.et, ISSN 7-7, EISSN 7-64. Variatioal Approach of Maragoi Mied Covectio Boudary Layer Flow with Pade Techique

More information

Effects of Chemical Reaction Heat and Mass Transfer on MHD Flow Past A Semi Infinite Plate with Viscous Dissipation

Effects of Chemical Reaction Heat and Mass Transfer on MHD Flow Past A Semi Infinite Plate with Viscous Dissipation Iteratioal Joural o Mechaical Egieerig ad Robotics (IJMER) Eects o Chemical Reactio Heat ad Mass Traser o MHD Flo Past A Semi Iiite Plate ith Viscous Dissipatio 1 K. Govardha, B S Malga, N. Kisha, 4 P.

More information

ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS

ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS Sudarapadia Vaidyaatha Research ad Developmet Cetre, Vel Tech Dr. RR & Dr. SR Techical Uiversity Avadi, Cheai-600 062, Tamil Nadu,

More information

DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS

DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS Ivaa Štimac 1, Ivica Kožar 1 M.Sc,Assistat, Ph.D. Professor 1, Faculty of Civil Egieerig, Uiverity of Rieka, Croatia INTRODUCTION The vehicle-iduced

More information

The Analysis of the Non-linear Deflection of Non-straight Ludwick type Beams Using Lie Symmetry Groups

The Analysis of the Non-linear Deflection of Non-straight Ludwick type Beams Using Lie Symmetry Groups Proceedigs of the 3 rd Iteratioal Coferece o Cotrol, Dyamic Systems, ad Robotics CDSR 16 Ottawa, Caada May 9 10, 016 Paper No. 107 DOI: 10.11159/cdsr16.107 The Aalysis of the No-liear Deflectio of No-straight

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

Available online European Journal of Advances in Engineering and Technology, 2018, 5(3):

Available online   European Journal of Advances in Engineering and Technology, 2018, 5(3): Available olie www.ejaet.com Europea Joural of Advaces i Egieerig ad Techology, 018, 5(3): 14-150 Research Article ISSN: 394-658X Iclied Magetic Field ad Viscous Dissipatio Effects o Taget Hyperbolic Naofluid

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

Research Article Revisiting Blasius Flow by Fixed Point Method

Research Article Revisiting Blasius Flow by Fixed Point Method Abstract ad Applied Aalysis, Article ID 953151, 9 pages http://dx.doi.org/10.1155/2014/953151 Research Article Revisitig Blasius Flow by Fixed Poit Method Dig Xu, 1 Jiglei Xu, 2 ad Goga Xie 3 1 State Key

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

Effect of Radial Magnetic Field on Free Convective Flow over Ramped Velocity Moving Vertical Cylinder with Ramped Type Temperature and Concentration

Effect of Radial Magnetic Field on Free Convective Flow over Ramped Velocity Moving Vertical Cylinder with Ramped Type Temperature and Concentration Joural of Applied Fluid Mechaics, Vol. 9, No. 6, pp. 2855-2864, 2016. Available olie at www.jafmolie.et, ISSN 1735-3572, EISSN 1735-3645. Effect of Radial Magetic Field o Free Covective Flow over Ramped

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

MHD Flow of a Third-Grade Fluid Induced by Non-Coaxial Rotations of a Porous Disk Executing Non-Torsional Oscillations and a Fluid at Infinity

MHD Flow of a Third-Grade Fluid Induced by Non-Coaxial Rotations of a Porous Disk Executing Non-Torsional Oscillations and a Fluid at Infinity MHD Flow of a Third-Grade Fluid Iduced by No-Coaxial Rotatios of a Porous Disk Executig No-Torsioal Oscillatios ad a Fluid at Ifiity TAHIRA HAROON COMSATS Istitute of Iformatio Techology, Abbottabad, NWFP,

More information

THE STUDY OF HEAT TRANSFER PHENOMENA BY USING MODIFIED HOMOTOPY PERTURBATION METHOD COUPLED BY LAPLACE TRANSFORM

THE STUDY OF HEAT TRANSFER PHENOMENA BY USING MODIFIED HOMOTOPY PERTURBATION METHOD COUPLED BY LAPLACE TRANSFORM THE STUDY OF HEAT TRANSFER PHENOMENA BY USING MODIFIED HOMOTOPY PERTURBATION METHOD COUPLED BY LAPLACE TRANSFORM Uriel FILOBELLO-NINO, Hector VAZQUEZ-LEAL *, Agusti Leobardo HERRERA-MAY,,3, Roberto Carlos

More information

Application of Homotopy Analysis Method for Water Transport in Unsaturated Porous Media

Application of Homotopy Analysis Method for Water Transport in Unsaturated Porous Media Studies i Noliear Scieces 1 (1): 8-1, 1 ISSN 1-91 IDOSI Publicatios, 1 Applicatio of Homotopy Aalysis Method for Water Trasport i Usaturated Porous Media Hossei Jafari ad M.A. Firoozjaee Departmet of Mathematics,

More information

Implicit Finite Difference Solution of MHD Boundary Layer Heat Transfer over a Moving plate

Implicit Finite Difference Solution of MHD Boundary Layer Heat Transfer over a Moving plate IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:39-765x. Volume 9, Issue 3 (Nov. Dec. 03), PP 8-3.iosrournals.org Implicit Finite Difference Solution of MHD Boundary Layer Heat Transfer over

More information

Free Surface Hydrodynamics

Free Surface Hydrodynamics Water Sciece ad Egieerig Free Surface Hydrodyamics y A part of Module : Hydraulics ad Hydrology Water Sciece ad Egieerig Dr. Shreedhar Maskey Seior Lecturer UNESCO-IHE Istitute for Water Educatio S. Maskey

More information

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS Please cite this article as: Staisław Kula, Method of fudametal solutios for Helmholtz eigevalue problems i elliptical domais, Scietific Research of the Istitute of Mathematics ad Computer Sciece, 009,

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

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

High-Precision Direct Method for the Radiative Transfer Problems

High-Precision Direct Method for the Radiative Transfer Problems Commu. Theor. Phys. 59 201 782 788 Vol. 59, No. 6, Jue 15, 201 High-Precisio Direct Method for the Radiative Trasfer Problems ZHANG Ya, 1 HOU Su-Qig ã, 2, YANG Pig, 1 ad WU Kai-Su Ñ 1, 1 Beijig Uiversity

More information

Unsteady Couette Flow through a Porous Medium in a Rotating System

Unsteady Couette Flow through a Porous Medium in a Rotating System Ope Joural of Fluid Dyamics, 0,, 49-58 http://d.doi.org/0.436/ojfd.0.406 Published Olie December 0 (http://www.scirp.org/joural/ojfd) Usteady Couette Flow through a Porous Medium i a Rotatig System Maitree

More information

Computational Fluid Dynamics. Lecture 3

Computational Fluid Dynamics. Lecture 3 Computatioal Fluid Dyamics Lecture 3 Discretizatio Cotiued. A fourth order approximatio to f x ca be foud usig Taylor Series. ( + ) + ( + ) + + ( ) + ( ) = a f x x b f x x c f x d f x x e f x x f x 0 0

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

Journal of Computational Physics 149, (1999) Article ID jcph , available online at

Journal of Computational Physics 149, (1999) Article ID jcph , available online at Joural of Computatioal Physics 149, 418 422 (1999) Article ID jcph.1998.6131, available olie at http://www.idealibrary.com o NOTE Defiig Wave Amplitude i Characteristic Boudary Coditios Key Words: Euler

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

Implicit Finite Difference Solution of Boundary Layer Heat Flow over a Flat Plate

Implicit Finite Difference Solution of Boundary Layer Heat Flow over a Flat Plate ISSN : 48-96, Vol. 3, Issue 6, Nov-Dec 03, 6-66 www.iera.com RESEARCH ARTICLE OPEN ACCESS Implicit Finite Difference Solution of Boundary Layer Heat Flow over a Flat Plate Satish V Desale*, V.H.Pradhan**

More information

Some properties of Boubaker polynomials and applications

Some properties of Boubaker polynomials and applications Some properties of Boubaker polyomials ad applicatios Gradimir V. Milovaović ad Duša Joksimović Citatio: AIP Cof. Proc. 179, 1050 (2012); doi: 10.1063/1.756326 View olie: http://dx.doi.org/10.1063/1.756326

More information

Numerical Methods in Geophysics: Implicit Methods

Numerical Methods in Geophysics: Implicit Methods Numerical Methods i Geophysics: What is a implicit scheme? Explicit vs. implicit scheme for Newtoia oolig rak-nicholso Scheme (mixed explicit-implicit Explicit vs. implicit for the diffusio equatio Relaxatio

More information

Analysis of a Numerical Scheme An Example

Analysis of a Numerical Scheme An Example http://www.d.edu/~gtryggva/cfd-course/ Computatioal Fluid Dyamics Lecture 3 Jauary 5, 7 Aalysis of a Numerical Scheme A Example Grétar Tryggvaso Numerical Aalysis Example Use the leap-frog method (cetered

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

Numerical Study on the Boundary Value Problem by Using a Shooting Method

Numerical Study on the Boundary Value Problem by Using a Shooting Method Pure ad Applied Mathematics Joural 2015; 4(3: 9-100 Published olie May 25, 2015 (http://www.sciecepublishiggroup.com/j/pamj doi: 10.1148/j.pamj.20150403.1 SSN: 232-9790 (Prit; SSN: 232-9812 (Olie Numerical

More information

Analysis and Numerical Approximation of a Singular Boundary Value Problem for the One-dimensional p-laplacian

Analysis and Numerical Approximation of a Singular Boundary Value Problem for the One-dimensional p-laplacian Proceedigs of the 4th WSEAS Iteratioal Coferece o Fluid Mechaics Gold Coast Queeslad Australia Jauary 7-9 007 4 Aalysis ad Numerical Approximatio of a Sigular Boudary Value Problem for the Oe-dimesioal

More information

Using Spreadsheets as a Computational Tool in Teaching Mechanical. Engineering

Using Spreadsheets as a Computational Tool in Teaching Mechanical. Engineering Proceedigs of the th WSEAS Iteratioal Coferece o COMPUTERS, Vouliagmei, Athes, Greece, July 3-5, 6 (pp35-3) Usig Spreadsheets as a Computatioal Tool i Teachig Mechaical Egieerig AHMADI-BROOGHANI, ZAHRA

More information

TMA4205 Numerical Linear Algebra. The Poisson problem in R 2 : diagonalization methods

TMA4205 Numerical Linear Algebra. The Poisson problem in R 2 : diagonalization methods TMA4205 Numerical Liear Algebra The Poisso problem i R 2 : diagoalizatio methods September 3, 2007 c Eiar M Røquist Departmet of Mathematical Scieces NTNU, N-749 Trodheim, Norway All rights reserved A

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

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

Steady symmetrical temperature field in a hollow spherical particle with temperature-dependent thermal conductivity

Steady symmetrical temperature field in a hollow spherical particle with temperature-dependent thermal conductivity Arch. Mech., 64, 4, pp. 45 422, Warszawa 212 Steady symmetrical temperature field i a hollow spherical particle with temperature-depedet thermal coductivity A. MOOSAIE Departmet of Mechaical Egieerig Yasouj

More information

Special Modeling Techniques

Special Modeling Techniques Colorado School of Mies CHEN43 Secial Modelig Techiques Secial Modelig Techiques Summary of Toics Deviatio Variables No-Liear Differetial Equatios 3 Liearizatio of ODEs for Aroximate Solutios 4 Coversio

More information

Solution of Lane-Emden Equation by Differential Transform Method

Solution of Lane-Emden Equation by Differential Transform Method ISSN 1749-3889 (prit), 1749-3897 (olie) Iteratioal Joural of Noliear Sciece Vol.12(2011) No.4,pp.478-484 Solutio of Lae-Emde Equatio by Differetial Trasform Method Supriya Mukherjee 1, Baamali Roy 2, Pratik

More information

Chapter 2: Numerical Methods

Chapter 2: Numerical Methods Chapter : Numerical Methods. Some Numerical Methods for st Order ODEs I this sectio, a summar of essetial features of umerical methods related to solutios of ordiar differetial equatios is give. I geeral,

More information

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations Global Joural of Sciece Frotier Research Mathematics ad Decisio Scieces Volume 3 Issue Versio 0 Year 03 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic (USA Olie

More information

A COMPLEX VARIABLE BOUNDARY ELEMENT METHOD FOR AN ELLIPTIC PARTIAL DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS

A COMPLEX VARIABLE BOUNDARY ELEMENT METHOD FOR AN ELLIPTIC PARTIAL DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS A COMPLEX VARIABLE BOUNDARY ELEMENT METHOD FOR AN ELLIPTIC PARTIAL DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS Y. S. PARK a adw.t.ang b Computatioal ad Mathematical Scieces Group Faculty of Iformatio

More information

A mathematical model of blood flow through diseased blood vessel

A mathematical model of blood flow through diseased blood vessel Iteratioal Joural of Emergig Treds & Techology i Computer Sciece (IJETTCS Volume 6, Issue 3, May- Jue 27 ISSN 2278-6856 A mathematical model of blood flow through diseased blood vessel Sapa Rata Shah,

More information

Explicit Group Methods in the Solution of the 2-D Convection-Diffusion Equations

Explicit Group Methods in the Solution of the 2-D Convection-Diffusion Equations Proceedigs of the World Cogress o Egieerig 00 Vol III WCE 00 Jue 0 - July 00 Lodo U.K. Explicit Group Methods i the Solutio of the -D Covectio-Diffusio Equatios a Kah Bee orhashidah Hj. M. Ali ad Choi-Hog

More information

Hydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields

Hydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields Hydroge (atoms, molecules) i exteral fields Static electric ad magetic fields Oscyllatig electromagetic fields Everythig said up to ow has to be modified more or less strogly if we cosider atoms (ad ios)

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

A note on the modified Hermitian and skew-hermitian splitting methods for non-hermitian positive definite linear systems

A note on the modified Hermitian and skew-hermitian splitting methods for non-hermitian positive definite linear systems A ote o the modified Hermitia ad skew-hermitia splittig methods for o-hermitia positive defiite liear systems Shi-Liag Wu Tig-Zhu Huag School of Applied Mathematics Uiversity of Electroic Sciece ad Techology

More information

A Primal-Dual Interior-Point Filter Method for Nonlinear Semidefinite Programming

A Primal-Dual Interior-Point Filter Method for Nonlinear Semidefinite Programming The 7th Iteratioal Symposium o Operatios Research ad Its Applicatios (ISORA 8) Lijiag, Chia, October 31 Novemver 3, 28 Copyright 28 ORSC & APORC, pp. 112 118 A Primal-Dual Iterior-Poit Filter Method for

More information

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet

More information

Temperature Distribution in a Cylindrical Core and Coil Assembly with Heat Generation

Temperature Distribution in a Cylindrical Core and Coil Assembly with Heat Generation Temperature Distributio i a Cylidrical Core ad Coil Assembly with Heat Geeratio P. S. Yeh, Ph.D. Abstract A residetial distributio trasformer cosists of a cylidrical steel tak ad a core-ad-coil assembly

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

Taylor expansion: Show that the TE of f(x)= sin(x) around. sin(x) = x - + 3! 5! L 7 & 8: MHD/ZAH

Taylor expansion: Show that the TE of f(x)= sin(x) around. sin(x) = x - + 3! 5! L 7 & 8: MHD/ZAH Taylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. A ay poit i the eighbourhood of 0, the fuctio ƒ() ca be represeted by a power series of the followig form: X 0 f(a) f() f() ( ) f( ) ( )

More information

AE/ME 339 Computational Fluid Dynamics (CFD)

AE/ME 339 Computational Fluid Dynamics (CFD) AE/ME 339 Computatioal Fluid Dyamics (CFD 0//004 Topic0_PresCorr_ Computatioal Fluid Dyamics (AE/ME 339 Pressure Correctio Method The pressure correctio formula (6.8.4 Calculatio of p. Coservatio form

More information

The Small Scale Effect on the Dynamic Behavior of Cantilever and Fixed-Fixed Nano-Switches

The Small Scale Effect on the Dynamic Behavior of Cantilever and Fixed-Fixed Nano-Switches Iteratioal Joural of Modelig ad Optimizatio, Vol. 4, No. 6, December 4 The Small Scale Effect o the Dyamic Behavior of Catilever ad Fixed-Fixed Nao-Switches B. Che,. Ta, ad Z. Y. Ou Abstract Based o the

More information

Algebra of Least Squares

Algebra of Least Squares October 19, 2018 Algebra of Least Squares Geometry of Least Squares Recall that out data is like a table [Y X] where Y collects observatios o the depedet variable Y ad X collects observatios o the k-dimesioal

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

Machine Learning Brett Bernstein

Machine Learning Brett Bernstein Machie Learig Brett Berstei Week 2 Lecture: Cocept Check Exercises Starred problems are optioal. Excess Risk Decompositio 1. Let X = Y = {1, 2,..., 10}, A = {1,..., 10, 11} ad suppose the data distributio

More information

SECOND-LAW ANALYSIS OF LAMINAR NON- NEWTONIAN GRAVITY-DRIVEN LIQUID FILM ALONG AN INCLINED HEATED PLATE WITH VISCOUS DISSIPATION EFFECT

SECOND-LAW ANALYSIS OF LAMINAR NON- NEWTONIAN GRAVITY-DRIVEN LIQUID FILM ALONG AN INCLINED HEATED PLATE WITH VISCOUS DISSIPATION EFFECT Brazilia Joural of Chemical Egieerig ISSN -663 Prited i Brazil www.abeq.org.br/bjche Vol. 6, No., pp. 7 -, April - Jue, 9 SECOND-LAW ANALSIS OF LAMINAR NON- NEWTONIAN GRAVIT-DRIVEN LIQUID FILM ALONG AN

More information

Numerical Solution of the First-Order Hyperbolic Partial Differential Equation with Point-Wise Advance

Numerical Solution of the First-Order Hyperbolic Partial Differential Equation with Point-Wise Advance Iteratioal oural of Sciece ad Research (ISR) ISSN (Olie): 39-74 Ide Copericus Value (3): 4 Impact Factor (3): 4438 Numerical Solutio of the First-Order Hyperbolic Partial Differetial Equatio with Poit-Wise

More information