Modeling of nonstationary heat and mass transfer processes in multilayered media based on hybrid numerical-analytical methods

The paper addresses the mathematical modeling of nonstationary heat and mass transfer processes in multilayered media with discontinuous thermophysical properties at the layer interfaces. A hybrid numerical-analytical method is proposed, combining finite-difference approximation in the spatial variable with the integral Laplace transform in time. This approach yields a semi-analytical solution in the transform domain, followed by numerical inversion of the Laplace transform with controlled accuracy. Computational experiments are performed for two-layer and three-layer domains with various boundary conditions and internal heat sources. It is demonstrated that the proposed method provides higher accuracy compared to purely difference schemes at comparable computational costs, especially in problems with stiff coefficients. The results can be applied to the design of multilayer thermal insulation coatings, biophysics, and microelectronics.