A family of new fourth-order solvers for a nonlinear damped wave equation

作者：Deng, Dingwen^*; Zhang, Chengjian

来源：Computer Physics Communications, 2013, 184(1): 86-101.

DOI：10.1016/j.cpc.2012.08.019

• Damped wave equation
• Compact finite difference scheme
• ADI method
• Richardson extrapolation algorithm
• Convergence analysis

In this paper, we propose a family of new three-level compact alternating direction implicit (ADI) difference schemes for solving a linear wave equation with a nonlinear damping function. By using a fourth-order accurate scheme to approximate the exact solution at the first time level, it is shown through the energy method that these difference schemes have fourth-order accuracy in space and second-order accuracy in time with respect to H-1- and L-infinity-norms. A class of Richardson extrapolation algorithms based on three time-grid parameters are presented to obtain approximate solution of fourth-order accuracy in both time and space in L-infinity-norm. Numerical experiments are performed to support our theoretical results and test the accuracy and efficiency of our algorithms.

• 出版日期2013-1
• 单位华中科技大学; 南昌航空大学