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The paper develops numerical solution methods for heat conduction boundary value problems for the case of the power dependence of the heat conductivity factor on temperature. Besides heat distribution in space, it describes filtration of a polytrophic gas in a porous medium. A distinctive feature of this equation is the degeneration of its parabolic type when the required function becomes zero, whereupon the equation acquires some properties typical of first-order equations. Particularly, in some cases, it proves possible to substantiate theorems of the existence and uniqueness of heat-wave type solutions for it. A numerical method using the advantages of the power series method and the boundary element method is proposed for the solution of the boundary value problem with a specified heat wave front. Simultaneous application of the two methods allows the accuracy of the numerical solution to be increased. A program has been developed from the proposed method. Test examples are considered.

Simultenious application of the boundary element method and the power series method for solving a two-dimensional problem of heat wave motion