Finite difference approximation for the 2d heat equation with concentrated capacity

Abstract

© 2018, University of Nis. All rights reserved. The convergence of difference scheme for two-dimensional initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficients of the space derivatives, is considered. An estimate of the rate of convergence in a special discrete Sobolev norms, compatible with the smoothness of the coefficients and solution, is proved.