广义Zakharov-Kuznetsov方程的若干能量守恒算法

SOME ENERGY CONSERVATIVE ALGORITHMS FOR GENERALIZED ZAKHAROV-KUZNETSOV EQUATION

本文基于哈密尔顿偏微分方程的多辛形式,利用平均值离散梯度构造了若干二维广义Zakharov-Kuznetsov方程的能量守恒算法,包括一个局部能量守恒算法及一个整体能量守恒算法.并证明了在周期边界条件下,两个格式均保持离散整体能量.数值例子验证了方法的有效性及正确性.

In this paper, based on multi-symplectic formulation of Hamiltonian PDEs, we develop several energy conservative algorithms for two-dimensional generalized Zakharov-Kuznetsov equation by using the mean value discrete gradient, including a local energy conservative algorithm and a global energy conservative algorithm. We prove that both schemes preserve the discrete global energy under periodic boundary conditions. Numerical experiments are presented to verify the efficiency and accuracy of the method.