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, Improved Boussinesq equation, Stokes
damping, Hydrodynamic damping, Runge-Kutta method.
AB - <p style="text-align: justify;">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.</p>