Numerical algorithms for one parabolic-elliptic problem
Articles
Raimondas Čiegis
Vilnius Gediminas Technical University
Remigijus Čiegis
Vilnius University
Published 2003-12-22
https://doi.org/10.15388/LMR.2003.32532
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How to Cite

Čiegis, R. and Čiegis, R. (2003) “Numerical algorithms for one parabolic-elliptic problem”, Lietuvos matematikos rinkinys, 43(spec.), pp. 581–585. doi:10.15388/LMR.2003.32532.

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.

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