数学
无量纲量
极限(数学)
曲柄-尼科尔森法
空格(标点符号)
类型(生物学)
有限差分
数学分析
有限差分法
应用数学
物理
机械
生态学
生物
语言学
哲学
作者
Tingchun Wang,Zhuo Yang
摘要
In this paper, we use the order reduction method to present a Crank–Nicolson‐type finite difference scheme for Zakharov system (ZS) with a dimensionless parameter , which is inversely proportional to the ion acoustic speed. The proposed scheme is proved to perfectly inherit the mass and energy conservation possessed by ZS, while the invariants satisfied by most existing schemes are expressed by two‐level's solution at each time step. In the subsonic limit regime, that is, when , the solution of ZS propagates rapidly oscillatory initial layers in time, and this brings significant difficulties in designing numerical methods and establishing the error estimates, especially in the subsonic limit regime. After proving the solvability of the proposed scheme, we use the cut‐off function technique and energy method to rigorously analyze two independent error estimates for the well‐prepared, less‐ill‐prepared, ill‐prepared initial data, respectively, which are uniform in both time and space for and optimal at second order in space. Numerical examples are carried out to verify the theoretical results and show the effectiveness of the proposed scheme.
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