A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations
A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations
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DOI：
10.1016/s0377-0427(98)00006-5
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发表时间：
1998-04
影响因子：
2.4
通讯作者：
B. Feng;T. Mitsui
中科院分区：
文献类型：
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作者：
B. Feng;T. Mitsui
提出了求解Korteweg-de Vries方程的一种线性化隐式有限差分方法，并将其推广到Kadomtsev-Petviashvili方程。研究了该方法的精度阶数，并证明了该方法是无条件线性稳定的。对Korteweg-de Vries方程和Kadomtsev-Petviashvili方程进行了不同条件下的数值实验。本文还报道了Kadomtsev-Petviashvili方程两个块状孤立波解碰撞的数值结果。
A linearized implicit finite difference method for the Korteweg-de Vries equation is proposed and straightforwardly extended to the Kadomtsev-Petviashvili equation. We investigate the order of accuracy of the method and prove the method to be unconditionally linearly stable. The numerical experiments for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations are carried out with various conditions. Numerical results for the collision of two lump type solitary wave solutions to the Kadomtsev-Petviashvili equation are also reported.