An efficient algorithm for the numerical solution of a three-dimensional thermal conductivity issue

A mathematical model of slab heating based on a numerical solution of a three-dimensional thermal conductivity problem has been created and programmatically implemented in the work. To solve a system of difference equations, a layer-by-layer method is proposed that allows using the run-through method to solve a system of difference equations of a three-dimensional problem within a rapidly converging iterative procedure. Comparative calculations of slab heating are carried out using the proposed layer-by-layer method and the method of simple iteration with different degrees of grinding of the spatial grid. As a result, it was found that with the grinding of the mesh, the effectiveness of the layered method in relation to the simple iteration method increases.