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

摘要

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 L2-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.