解一类高阶非线性波动方程的数值方法及理论分析

The Numerical Method and Theoretical Analysis for a Class of Third-Order Nonlinear Wave Equations

对一类三阶非线性波动方程建立了2个时间差分离散隐格式,利用再生核函数将每个时间层上的近似解表示成显式的积分形式,并用能量估计的方法证明了这2种差分格式的稳定性和收敛性,最后给出了一些数值结果。

In this paper,we build two time difference discrete implicit schemes for a class of third-order nonlinear wave equations.And by using the reproducing kernel function,the approximate solution of each time layer is expressed in explicit integral form.Then by using the energy method,the convergence and stability of the schemes are proved.Finally some numerical results are presented.