A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations |
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Affiliation: | 1. Department of Aeronautics and Astronautics, Kyoto University, Kyoto 606-01, Japan;2. Graduate School of Human Informatics, Nagoya University, Nagoya 464-01, Japan |
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Abstract: | 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. |
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