The initial-boundary value problem for the three-dimensional heat equation solved by Rothe's line method using integral equations

A solution of the initial-boundary value problem for the three-dimensional heat equation in a compact domain with a boundary of continuous curvature is sought. Rothe's line method, which works by discretization of the time variable is used. For every time step there remains an elliptic boundary value problem, which is solved by means of an integral equation. The approximate solutions converge to the exact solution of the original problem. In case of a sphere one finds a simple error estimate for the approximation. For two initial conditions the practical computations show that the integral equations method yields useful results with relative small effort.