Linear B-spline finite element method for the improved Boussinesq equation

Authors:
Qun Lin;Yong Hong Wu;Ryan Loxton;Shaoyong Lai
Affiliations:
Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;Department of Economic Mathematics, South Western University of Finance and Economics, Chengdu, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
Cited 0

Nonlinear partial differential equations: for scientists and engineers

Nonlinear partial differential equations: for scientists and engineers
On exact travelling wave solutions for two types of nonlinear K(n,n) equations and a generalized KP equation

Journal of Computational and Applied Mathematics
Nonlinear variants of the improved Boussinesq equation with compact and noncompact structures

Computers & Mathematics with Applications

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Abstract

In this paper, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the nonlinear partial differential equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem to which many accurate numerical methods are readily applicable. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior.