Zakharov系统的一个局部动量守恒算法

A LOCAL MOMENTUM-PRESERVING ALGORITHM FOR THE ZAKHAROV SYSTEM

基于“数值算法应尽可能地保持原问题的本质特征”这一思想,本文利用复合构造方法为Zakharov系统构造了一个局部动量守恒算法.本文所提出格式的优点是它在任何时空区域都能够保持局部动量守恒和局部质量守恒,即不依赖于任何的边界条件.在合适的边界条件下,例如齐次边界条件和周期边界条件,所提出的算法也保持了全局的动量守恒和质量守恒.数值实验给出了算法的时空二阶收敛性,并且验证了该算法的长时间计算稳定性和不变量守恒性.

In this paper,we use the concatenating method to construct a local momentum-preserving algorithm for the Zakharov system based on the idea that the numerical algorithm should keep the intrinsic properties of the original problem as much as possible.The advantage of the proposed algorithm is that it preserves the local momentum conservation law and the local mass conservation law in any time-space regions,i.e.,independence on any boundary conditions.Certainly,if the boundary condition is suitable,such as homogeneous boundary or periodic boundary,the proposed algorithm also preserves the global momentum conser-vation law and the global mass conservation law.Numerical experiments do not only show the second-order convergence,but also verify the stability in long term calculations and the conservation of invariants for the proposed algorithm.