Volume 31, Issue 3
Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation

Abdelhamid Bezia and Anouar Ben Mabrouk

10.4208/jpde.v31.n3.1

J. Part. Diff. Eq., 31 (2018), pp. 193-213.

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  • Abstract

This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov-Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

  • History

Published online: 2018-09

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