Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs

Ishak Hashim, M. S H Chowdhury

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.

Original languageEnglish
Pages (from-to)470-481
Number of pages12
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume372
Issue number4
DOIs
Publication statusPublished - 21 Jan 2008

Fingerprint

linear systems
nonlinear systems
perturbation
Runge-Kutta method
intervals

Keywords

  • Homotopy-perturbation method
  • Runge-Kutta method
  • System of ODEs

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs. / Hashim, Ishak; Chowdhury, M. S H.

In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 372, No. 4, 21.01.2008, p. 470-481.

Research output: Contribution to journalArticle

@article{50b6a899d4d549ce8206d3e465952bc5,
title = "Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs",
abstract = "A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.",
keywords = "Homotopy-perturbation method, Runge-Kutta method, System of ODEs",
author = "Ishak Hashim and Chowdhury, {M. S H}",
year = "2008",
month = "1",
day = "21",
doi = "10.1016/j.physleta.2007.07.067",
language = "English",
volume = "372",
pages = "470--481",
journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",
issn = "0375-9601",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs

AU - Hashim, Ishak

AU - Chowdhury, M. S H

PY - 2008/1/21

Y1 - 2008/1/21

N2 - A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.

AB - A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.

KW - Homotopy-perturbation method

KW - Runge-Kutta method

KW - System of ODEs

UR - http://www.scopus.com/inward/record.url?scp=37549072668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37549072668&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2007.07.067

DO - 10.1016/j.physleta.2007.07.067

M3 - Article

VL - 372

SP - 470

EP - 481

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 4

ER -