Application of the modified boundary element method for the solution of parabolic problems

Abstract

An algorithm for finding numerically-analytical solution of parabolic problems (diffusion and heat conduction) is proposed. The problem is solved by the proposed algorithm in three steps. At the first step the one-dimensional problem is solved for a base interval of integration. This problem is of independent significance as well as the basis for the second step. At the second step the two-dimensional parabolic problem is considered. Its solution is performed using the modified boundary elements method. At the third step, the method of step-by-step integration over time is used.