Lyapunov-Sylvester Computational Method for Two-Dimensional Boussinesq Equation

Abstract

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating Lyapunov-Sylvester operators. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

arXiv commentarXiv admin note: text overlap with arXiv:1011.1425, arXiv:1511.02358