Solving systems of ODEs by homotopy analysis method

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).

Original languageEnglish
Pages (from-to)2060-2070
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume13
Issue number10
DOIs
Publication statusPublished - Dec 2008

Fingerprint

Homotopy Analysis Method
Runge Kutta methods
Chaotic systems
System of Ordinary Differential Equations
Ordinary differential equations
Differential equations
differential equations
Stiff Systems
Runge-Kutta method
Runge-Kutta Methods
Chaotic System
Analytical Solution
Differential equation
matrices

Keywords

  • Genesio system
  • Homotopy analysis method
  • Matrix Riccati differential equation
  • Nonlinearity
  • Stiff system

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

Solving systems of ODEs by homotopy analysis method. / Sami Bataineh, A.; Md. Noorani, Mohd. Salmi; Hashim, Ishak.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 10, 12.2008, p. 2060-2070.

Research output: Contribution to journalArticle

@article{82708704732049f88c94fbc8461db194,
title = "Solving systems of ODEs by homotopy analysis method",
abstract = "This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).",
keywords = "Genesio system, Homotopy analysis method, Matrix Riccati differential equation, Nonlinearity, Stiff system",
author = "{Sami Bataineh}, A. and {Md. Noorani}, {Mohd. Salmi} and Ishak Hashim",
year = "2008",
month = "12",
doi = "10.1016/j.cnsns.2007.05.026",
language = "English",
volume = "13",
pages = "2060--2070",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",
number = "10",

}

TY - JOUR

T1 - Solving systems of ODEs by homotopy analysis method

AU - Sami Bataineh, A.

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

PY - 2008/12

Y1 - 2008/12

N2 - This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).

AB - This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).

KW - Genesio system

KW - Homotopy analysis method

KW - Matrix Riccati differential equation

KW - Nonlinearity

KW - Stiff system

UR - http://www.scopus.com/inward/record.url?scp=43049183184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049183184&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2007.05.026

DO - 10.1016/j.cnsns.2007.05.026

M3 - Article

VL - 13

SP - 2060

EP - 2070

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 10

ER -