一类非线性波方程的TVD数值模拟研究

Numerical Study of a Class of Nonlinear Wave Equations by the TVD Scheme

考虑非线性波方程的初边值问题,应用高效稳定的TVD数值格式,结合实际数学物理问题,考虑不同的边界格式进行数值实验,揭示非线性系统的物理本质.通过几个算例进行验证,数值解与解析解十分吻合,数值实验表明该类方法适用于求解初边值非线性波方程.

The aim of this paper is to investigate a class of nonlinear wave equations by the TVD scheme. We validate the present scheme by some related problems where analytic solutions are available. It can be found that the numerical results agree well with the analytic solutions,which indicates that the present model is very effective and can be used to solve more general nonlinear wave problems.