A finite difference method for solving a degenerate equation

Several papers have dealt with parabolic equations degenerate inside a region. The existence and uniqueness of the solution of the first boundary value problem were proved in [1, 2] under very wide assumptions regarding the coefficients of the equation. Finite difference methods have previously only...

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Bibliographic Details
Published in:U.S.S.R. computational mathematics and mathematical physics 1970, Vol.10 (5), p.122-131
Main Author: Lelikova, E.F.
Format: Article
Language:English
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Summary:Several papers have dealt with parabolic equations degenerate inside a region. The existence and uniqueness of the solution of the first boundary value problem were proved in [1, 2] under very wide assumptions regarding the coefficients of the equation. Finite difference methods have previously only been considered for equations degenerate on a boundary [3]. The present paper describes a homogeneous difference scheme for one type of parabolic equation degenerate inside a region. Our main aim is to obtain a priori bounds for the solution of the difference scheme. These bounds enable us to prove the convergence of the solution of the difference scheme to the generalized solution. At the same time, we obtain an independent proof of the existence of a generalized solution for the first boundary value problem in this particular case, under weaker restrictions on the coefficients than in [1, 2].
ISSN:0041-5553
DOI:10.1016/0041-5553(70)90042-X