Lyapunov-Sylvester Computational Method for Two-Dimensional Boussinesq Equation
This work provides a new computational approach for solving a specific PDE, but the results are incremental and lack comparison to existing methods.
The authors develop a numerical method using generalized Lyapunov-Sylvester operators to solve the two-dimensional Boussinesq equation, proving unique solvability, stability, and convergence, with numerical tests validating the theory.
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.