Exact solution for linear and nonlinear systems of PDES by homotopy-perturbation method

M. S H Chowdhury, Ishak Hashim, A. F. Ismail, M. M. Rahman, S. Momani

Research output: Contribution to journalArticle

Abstract

In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.

Original languageEnglish
Pages (from-to)3295-3305
Number of pages11
JournalAustralian Journal of Basic and Applied Sciences
Volume5
Issue number12
Publication statusPublished - Dec 2011

Fingerprint

linear systems
nonlinear systems
perturbation
partial differential equations

Keywords

  • Exact solutions
  • Homotopy-perturbation method
  • System of PDEs

ASJC Scopus subject areas

  • General

Cite this

Exact solution for linear and nonlinear systems of PDES by homotopy-perturbation method. / Chowdhury, M. S H; Hashim, Ishak; Ismail, A. F.; Rahman, M. M.; Momani, S.

In: Australian Journal of Basic and Applied Sciences, Vol. 5, No. 12, 12.2011, p. 3295-3305.

Research output: Contribution to journalArticle

Chowdhury, M. S H ; Hashim, Ishak ; Ismail, A. F. ; Rahman, M. M. ; Momani, S. / Exact solution for linear and nonlinear systems of PDES by homotopy-perturbation method. In: Australian Journal of Basic and Applied Sciences. 2011 ; Vol. 5, No. 12. pp. 3295-3305.
@article{6ddf6e7fe3d644558237f4cfa3941bd8,
title = "Exact solution for linear and nonlinear systems of PDES by homotopy-perturbation method",
abstract = "In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.",
keywords = "Exact solutions, Homotopy-perturbation method, System of PDEs",
author = "Chowdhury, {M. S H} and Ishak Hashim and Ismail, {A. F.} and Rahman, {M. M.} and S. Momani",
year = "2011",
month = "12",
language = "English",
volume = "5",
pages = "3295--3305",
journal = "Australian Journal of Basic and Applied Sciences",
issn = "1991-8178",
publisher = "INSInet Publications",
number = "12",

}

TY - JOUR

T1 - Exact solution for linear and nonlinear systems of PDES by homotopy-perturbation method

AU - Chowdhury, M. S H

AU - Hashim, Ishak

AU - Ismail, A. F.

AU - Rahman, M. M.

AU - Momani, S.

PY - 2011/12

Y1 - 2011/12

N2 - In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.

AB - In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.

KW - Exact solutions

KW - Homotopy-perturbation method

KW - System of PDEs

UR - http://www.scopus.com/inward/record.url?scp=84856435548&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856435548&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 3295

EP - 3305

JO - Australian Journal of Basic and Applied Sciences

JF - Australian Journal of Basic and Applied Sciences

SN - 1991-8178

IS - 12

ER -