A new approximate analytical solution of kuramoto-Sivashinsky equation using homotopy analysis method

KURULAY M., SEÇER A., AKINLAR M. A.

Applied Mathematics and Information Sciences, vol.7, no.1, pp.267-271, 2013 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.12785/amis/070133
  • Journal Name: Applied Mathematics and Information Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.267-271
  • Keywords: Approximate analytical solutions, Homotopy analysis method, Kuramoto-Sivashinsky equation, Maple
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto-Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x; t), the initial guess, u0(x; t) and the auxiliary linear operator, L; as stated in [1]. The obtained results show that HAM yields approximate analytical solutions which are quite close to the exact solution of KS equation, which proves the strength of HAM. © 2013 NSP. Natural Sciences Publishing Cor.