Lyapunov-Sylvesters operators for (2+1)-Boussinesq equation

Abstract

This article studies a technique for solving a two-dimensional Boussinesq 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.

Keywords

• Boussinesq equation
• finite difference method
• Numerical solution
• Lyapunov-Sylvester operators