Mathematical model the first boundary value problem for a mixed equation thermal conductivity

The paper presents a computational model for solving the first boundary value problem for a partial differential equation of parabolic-hyperbolic type in a two-dimensional spatial case using explicit and implicit difference schemes. The mathematical model and these finite difference schemes are designed to study thermal processes when an electric arc is switched off in a satellite gas flow. The disadvantages of using the classical parabolic equation of thermal conductivity for this case are analyzed. The results of the work of programs implemented in MathCad-15, which allow us to calculate the change in the temperature field during a specified period of time in a rectangular area for variables in spatial coordinates and time of the lateral heat sink and internal heat source, are presented. To discretize the mixed thermal conductivity equation in time, the method of a locally one-dimensional scheme was used.