Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation
DOI:
https://doi.org/10.4208/jpde.v31.n3.1Keywords:
Kuramoto-Sivashinsky equation;Finite difference method;Lyapunov-Sylvester operators.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.
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Published
2018-09-20
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