带固定点源阻尼波动方程的有限差分法
Finite Difference Method for Damped Wave Equation with Fixed Point Source
DOI: 10.12677/aam.2026.154136, PDF,   
作者: 张潇腾:长沙理工大学数学与统计学院,湖南 长沙
关键词: 阻尼波动方程固定点源有限差分法Damped Wave Equation Fixed Source Finite Difference Method
摘要: 本文在周期边界条件下针对一类带有固定点源的阻尼波动方程提出了一种有限差分方法:在空间上采用中心差分格式进行近似,并在点源附近构造辅助函数进行修正,有效处理了解在该点的奇异性;在时间上则采用向后差分格式。数值实验结果验证了格式的有效性和收敛性。
Abstract: In this paper, a finite difference method is proposed for a class of damped wave equations with a fixed point source under periodic boundary conditions. The central difference scheme is used to approximate the space, and an auxiliary function is constructed near the point source to correct the singularity of the solution at this point. In time, the backward difference scheme is used. Numerical experimental results verify the effectiveness and convergence of the scheme.
文章引用:张潇腾. 带固定点源阻尼波动方程的有限差分法[J]. 应用数学进展, 2026, 15(4): 64-69. https://doi.org/10.12677/aam.2026.154136

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