Quadratic finite volume element method for the improved Boussinesq equation

Abstract

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.

Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method

“…In contrary of the references, we can conclude that for Amp ≤ 0.5 is clear and for Amp > 0.5 is not clear. The newly obtained results are same agreement with those studies in [4,11,15,17].…”

“…Shokri and Dehghan [14] by using collocation and radial basis functions have obtained approximate solutions. Zhang and Lu [17] have devised a quadratic finite volume scheme to solve the initial boundary value problem for the IBq.…”

A Numerical Study on Hydrodynamic Force Affecting the Vertical Wall of a Portable Water Storage Tank

“…소방용수 저장탱크 내의 유동 지배방정식을 아래 식 (1)과 같이 Boussinesq 방정식으로 표현할 수 있다(El-Zoheiry (2) ; Lin, Zhang and Lu (3) , Wu, Loxton and Lai (4) ).…”

New conservative finite volume element schemes for the modified Korteweg–de Vries equation

“…Perhaps, the most important property of FVEM is that it can preserve the conservation laws (mass, momentum, and heat flux) on each computational cell. This important property, in combination with adequate accuracy and ease of implementation, has attracted more people to do research in this f ield [19][20][21][22][23][24].…”