Numerical and Analytical Study of Processes Described by the Nonlinear Heat Equation

Abstract

The paper deals with one-dimensional boundary value problems for the nonlinear heat conduction (porous medium) equation in the case of a power law relationship between the heat conduction coefficient and temperature, the solution of which is a heat wave spreading along the cold background at the finite rate. A numerical algorithm of the solution obtained by the boundary element method is developed. Its software implementation is performed. Numerical calculations are carried out. Their results are compared to the known exact solutions of the considered equation, as well as to the multiple power series that are solutions of the investigated problem in case of the analyticity of the input data. The results reported here extend our previous work in this area.

Keywords

• partial differential equations
• nonlinear heat conduction equation
• boundary element method
• power series
• heat wave