Two-step numerical methods for a coupled parabolic-hyperbolic transmission problem

Abstract

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.