کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423105 | 1341248 | 2011 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs](/preview/png/6423105.png)
In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 6, 15 October 2011, Pages 1354-1369