Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation (Journal of Partial Differential Equations, 2018)
This paper investigates a solution technique for solving a two-dimensionalKuramoto-Sivashinsky equation discretized using a finite difference method. It consistsof 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-Sylvestermatrix equation. Convergence and stability is examined using Lyapunovcriterion and manipulating generalized Lyapunov-Sylvester operators. Some numericalimplementations are provided at the end to validate the theoretical results.
Keywords: Kuramoto-Sivashinsky equation; Finite difference method; Lyapunov-Sylvester operators.