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

Authors

Muhammet Kurulay, Yildiz Technical University, Faculty of Art and Sciences, Department of Mathematics, Istanbul, Turkey
Aydin Secer
Ali Akinlar

Author Country (or Countries)

Turkey

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.

Suggested Reviewers

N/A

Recommended Citation

Kurulay, Muhammet; Secer, Aydin; and Akinlar, Ali (2013) "A New Approximate Analytical Solution of Kuramoto – Sivashinsky Equation Using Homotopy Analysis Method," Applied Mathematics & Information Sciences: Vol. 07: Iss. 1, Article 33.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/33