Abstract

In this article is proposed a method for numerically solving a mixed problem for a hyperbolic equation with memory. An implicit difference scheme is constructed as an effective means for solving complex multidimensional problems of mathematical physics. A condition is found for guaranteed stability of an implicit difference scheme for a mixed problem in the \(L^{2}\)-norm. The order of convergence for all variables of the presented difference scheme was calculated and confirmed by numerical experiment.

中文翻译：

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双曲型记忆混合问题的隐式差分格式

摘要

本文提出了一种利用记忆数值求解双曲方程混合问题的方法。构造隐式差分格式作为解决数学物理复杂多维问题的有效手段。找到了保证 \(L^{2}\)范数中混合问题的隐式差分格式稳定性的条件。通过数值实验计算并证实了所提出的差分格式的所有变量的收敛阶。