Parabolinio-elipsinio uždavinio skaitinis sprendimas

Abstract

In this paper we solve numerically a parabolic-elliptic problem.Two finite difference schemes are proposed. The first scheme is a modification of the backward Euler algorithm and it requires to solve an elliptic problem at each time step.The spectral estimates of the obtained matrix are presented. The second scheme is a modification of the stability-correction scheme. This scheme is used as a classical splitting scheme in the parabolic region of the problem definition and as a new iterative algorithm in the elliptic part of the problem. We prove the convergence of the proposed scheme.