Kuramoto-Svashinsky方程的数值方法

Numerical methods for the Kuramoto-Svashinsky equation

给出一些线性化的时间差分/空间谱方法的数值格式,对非线性对流项进行了处理.格式的优点在于每次迭代只需要解一个线性方程.分析了格式的稳定性,并用数值结果证实了格式的有效性.讨论了K-S方程解的性质,及色散项对解的影响.

We construct several linearized finite difference/spectral methods for solving the K-S equation. A particular attention is paid to the treatment of the nonlinear convection term. A careful treatment of this term leads to some schemes which result in a linear equation to be solved at each time step. A numerical analysis is performed for the proposed schemes, and some discrete energy inequalities are obtained. Several numerical examples are used to validate the schemes. We finally apply the validated schemes to investigate the behavior of the solutions of the K-S equation,as well as the impact of the dispersive term on this behavior.