Solving a two-dimensional nonlinear heat conduction equation with nonzero boundary conditions by the boundary element method

摘要

The paper deals with an algorithm for solving two-dimensional boundary value problems for a nonlinear partial parabolic differential equation with degeneration. It discusses a problem of heat wave initiation under a boundary condition specified on a closed curve. The solution algorithm based on the boundary element method is proposed. Since the problem solution domain is unknown at each time moment, an interchange between the required function and the radial coordinate of polar coordinate system is used. The constructed algorithm is verified with the use of a known exact solution.