A Compact Fourth-Order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms
Year: 2016
Author: Fuqiang Lu, Zhiyao Song, Zhuo Zhang
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 462–478
Abstract
In this paper, a compact finite difference method is presented for solving the initial boundary value problems for the improved Boussinesq equation with damping terms. The fourth-order equation can be transformed into a first-order ordinary differential system, and then, the classical Padé approximation is used to discretize spatial derivative in the nonlinear partial differential equations. The resulting coefficient matrix for the semi-discrete scheme is tri-diagonal and can be solved efficiently. In order to maintain the same order of convergence, the classical fourth-order Runge-Kutta method is the preferred method for explicit time integration. Soliton-type solutions are used to evaluate the accuracy of the method, and various numerical experiments are designed to test the different effects of the damping terms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1603-m2014-0193
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 462–478
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Compact finite difference method Improved Boussinesq equation Stokes damping Hydrodynamic damping Runge-Kutta method.
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