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Pure Mathematics 2024
紧致有限差分方法求解全离散波动方程
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Abstract:
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).
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