# Approximate analytical solutions of systems of PDEs by homotopy analysis method

Research output: Contribution to journalArticle

43 Citations (Scopus)

### Abstract

In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

Original language English 2913-2923 11 Computers and Mathematics with Applications 55 12 https://doi.org/10.1016/j.camwa.2007.11.022 Published - Jun 2008

### Fingerprint

Homotopy Analysis Method
Systems of Partial Differential Equations
Partial differential equations
Analytical Solution
Series Solution
Variational Iteration Method
Second order differential equation
Partial differential equation
Nonlinear Systems
Linear Systems
First-order
Linear systems
Nonlinear systems

### Keywords

• Homotopy analysis method
• Nonlinear systems
• Systems of PDEs
• Variational iteration method

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Modelling and Simulation

### Cite this

In: Computers and Mathematics with Applications, Vol. 55, No. 12, 06.2008, p. 2913-2923.

Research output: Contribution to journalArticle

title = "Approximate analytical solutions of systems of PDEs by homotopy analysis method",
abstract = "In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.",
keywords = "Adomian decomposition method, Homotopy analysis method, Nonlinear systems, Systems of PDEs, Variational iteration method",
author = "{Sami Bataineh}, A. and {Md. Noorani}, {Mohd. Salmi} and Ishak Hashim",
year = "2008",
month = "6",
doi = "10.1016/j.camwa.2007.11.022",
language = "English",
volume = "55",
pages = "2913--2923",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",
number = "12",

}

TY - JOUR

T1 - Approximate analytical solutions of systems of PDEs by homotopy analysis method

AU - Sami Bataineh, A.

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

PY - 2008/6

Y1 - 2008/6

N2 - In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

AB - In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

KW - Homotopy analysis method

KW - Nonlinear systems

KW - Systems of PDEs

KW - Variational iteration method

UR - http://www.scopus.com/inward/record.url?scp=42749084915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42749084915&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2007.11.022

DO - 10.1016/j.camwa.2007.11.022

M3 - Article

AN - SCOPUS:42749084915

VL - 55

SP - 2913

EP - 2923

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 12

ER -