紧致有限差分方法求解全离散波动方程  

Compact Finite Difference Method for Solving Fully Discrete Wave Equations

作　　者：安文静 龙艳[1] 

机构地区：[1]新疆应用职业技术学院师范教育系,新疆 奎屯

出　　处：《理论数学》2024年第5期509-518,共10页Pure Mathematics

摘　　要：本文针对整数阶波动方程,给出了一种基于紧致有限差分方法的隐式全离散格式。该格式在时间方向采用中心差分格式来离散,在空间方向采用紧致中心差商的权平均来离散。离散格式的稳定性分析及误差估计表明,该离散格式在时间方向达到二阶收敛,空间方向达到四阶收敛。并且通过数值实验证明该离散格式的收敛阶为O(τ2h4)。This article proposes an implicit fully discrete scheme based on the compact finite difference method for integer order wave equations. This discretization scheme uses a central difference scheme for discretization in the temporal direction and a compact central difference quotient weighted average for discretization in the spatial direction. The stability analysis and error estimation of the discrete format indicate that it achieves second-order convergence in the temporal direction and fourth-order convergence in the spatial direction. And numerical experiments have shown that the convergence order of the discrete format isO(τ2h4).

关 键 词：波动方程 紧致有限差分法 稳定性 误差估计 

分 类 号：O17[理学—数学]