L2-stability analysis of novel ETD scheme for Kuramoto-Sivashinsky equations

Authors:
N. Vaissmoradi;A. Malek;S. H. Momeni-Masuleh
Affiliations:
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, POBox:14115-134, Iran;Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, POBox:14115-134, Iran;Department of Mathematics, Shahed University, Tehran, POBox:18151-159, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The aim of this paper is to study the stability analysis of novel ETD scheme proposed by the authors based on spectral methods, the exponential time differencing and Taylor expansion. Stability issue of the proposed numerical scheme is related to an analysis of the stability of the corresponding ODE system for time marching approach. It is proved that the novel scheme is L^2-stable in solving the Kuramoto-Sivashinsky model problems. The truncation error and the stability region for the novel scheme are provided. Comparisons with available literature are made.