Series solution for painlevé equation ii

Fazle Mabood, Waqar Ahmad Khan, Ahmad Izani Md Ismail, Ishak Hashim

Research output: Contribution to journalArticle

Abstract

The Painlev'e equations are second order ordinary differential equations which can be grouped into six families, namely Painlev'e equation I, II,…, VI. This paper presents the series solution of second Painlevé equation via optimal homotopy asymptotic method (OHAM). This approach is highly efficient and it controls the convergence of the approximate solution. Comparison of the obtained solution via OHAM is provided with those obtained by Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), Sinc-collocation and Runge-Kutta 4 methods. It is revealed that there is an excellent agreement between OHAM and other published data which confirm the effectiveness of the OHAM.

Original languageEnglish
Pages (from-to)941-947
Number of pages7
JournalWalailak Journal of Science and Technology
Volume12
Issue number10
Publication statusPublished - 7 Apr 2015

Fingerprint

Homotopy Method
Series Solution
Asymptotic Methods
Homotopy Perturbation Method
Adomian Decomposition Method
Second-order Ordinary Differential Equations
Runge-Kutta
Collocation
Approximate Solution
Optimal Solution

Keywords

  • Nonlinear ODE
  • Optimal homotopy asymptotic method
  • Painlevé equation

ASJC Scopus subject areas

  • General

Cite this

Mabood, F., Khan, W. A., Ismail, A. I. M., & Hashim, I. (2015). Series solution for painlevé equation ii. Walailak Journal of Science and Technology, 12(10), 941-947.

Series solution for painlevé equation ii. / Mabood, Fazle; Khan, Waqar Ahmad; Ismail, Ahmad Izani Md; Hashim, Ishak.

In: Walailak Journal of Science and Technology, Vol. 12, No. 10, 07.04.2015, p. 941-947.

Research output: Contribution to journalArticle

Mabood, F, Khan, WA, Ismail, AIM & Hashim, I 2015, 'Series solution for painlevé equation ii', Walailak Journal of Science and Technology, vol. 12, no. 10, pp. 941-947.
Mabood, Fazle ; Khan, Waqar Ahmad ; Ismail, Ahmad Izani Md ; Hashim, Ishak. / Series solution for painlevé equation ii. In: Walailak Journal of Science and Technology. 2015 ; Vol. 12, No. 10. pp. 941-947.
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