Quadratic finite volume element method for the improved Boussinesq equation

In this paper, a new numerical procedure is developed for solving the initial boundary value problems for the improved Boussinesq equation. The quadratic finite volume element method is used to discretize the nonlinear partial differential equation in space and a system involving only time parameter is derived. The resulting coefficient matrix for the semi-discrete scheme is tridiagonal and can be solved efficiently. For time derivative terms, central difference approximation is preferred. Various numerical experiments are given to test and validate our method and show its capacity to simulate single-wave splitting, wave interaction, and blow-up behavior.