In this study, we propose two different approaches of a two-step method for solving a system combining the heat and the wave equations. Our focus centers on the transmission problem in two dimensions, with a primary objective of numerically characterizing the distribution of temperature and pressure. First we apply a semi-discretization with respect to time by using the Laguerre transformation. This leads to a sequence of elliptic problems that are fully discretized either by the boundary integral equation method or by the fundamental sequences method. The presented numerical examples justify the applicability and efficiency of both schemes.

中文翻译：

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耦合抛物线-双曲传输问题的两步数值方法


在这项研究中，我们提出了两种不同的两步法方法，用于求解结合热方程和波动方程的系统。我们的重点集中在两个维度的传输问题上，主要目标是对温度和压力的分布进行数值表征。首先，我们使用 Laguerre 变换对时间应用半离散化。这导致了一系列椭圆问题，这些问题通过边界积分方程法或基本序列法完全离散化。所提出的数值示例证明了这两种方案的适用性和有效性。