A New Approximate Analytical Solution of Kuramoto - Sivashinsky Equation Using Homotopy Analysis Method

Kurulay M., Secer A., Akinlar M. A.

APPLIED MATHEMATICS & INFORMATION SCIENCES, vol.7, pp.267-271, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7
  • Publication Date: 2013
  • Doi Number: 10.12785/amis/070133
  • Journal Name: APPLIED MATHEMATICS & INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.267-271
  • Keywords: Kuramoto-Sivashinsky equation, homotopy analysis method, approximate analytical solutions, Maple
  • Yıldız Technical 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, u(0) (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.