Volume 34, Issue 5
A Compact Fourth-Order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms

Fuqiang Lu, Zhiyao Song & Zhuo Zhang

DOI: 10.4208/jcm.1603-m2014-0193

J. Comp. Math., 34 (2016), pp. 462-478.

Published online: 2016-10

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  • 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.

  • Keywords

Compact finite difference method Improved Boussinesq equation Stokes damping Hydrodynamic damping Runge-Kutta method

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lufuqiang2000@163.com (Fuqiang Lu)

Zhiyaosong@sohu.com (Zhiyao Song)

mercury1214@126.com (Zhuo Zhang)

  • BibTex
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  • TXT
@Article{JCM-34-462, author = {Lu , Fuqiang and Song , Zhiyao and Zhang , Zhuo }, title = {A Compact Fourth-Order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1603-m2014-0193}, url = {http://global-sci.org/intro/article_detail/jcm/9807.html} }
TY - JOUR T1 - A Compact Fourth-Order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms AU - Lu , Fuqiang AU - Song , Zhiyao AU - Zhang , Zhuo JO - Journal of Computational Mathematics VL - 5 SP - 462 EP - 478 PY - 2016 DA - 2016/10 SN - 34 DO - http://doi.org/10.4208/jcm.1603-m2014-0193 UR - https://global-sci.org/intro/article_detail/jcm/9807.html KW - Compact finite difference method KW - Improved Boussinesq equation KW - Stokes damping KW - Hydrodynamic damping KW - Runge-Kutta method AB - 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.
Fuqiang Lu , Zhiyao Song & Zhuo Zhang . (2020). A Compact Fourth-Order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms. Journal of Computational Mathematics. 34 (5). 462-478. doi:10.4208/jcm.1603-m2014-0193
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