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ICIAM/GAMM 95 Numerical Analysis, Scientific computing Computer ScienceICIAM/GAMM 95 Numerical Analysis, Scientific computing Computer Science
Author(s) -
Bochev, Mikhail A.
Publication year - 1996
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19960761109
Subject(s) - computer science , computational science , numerical analysis , mathematics , mathematical analysis
Solving numerically initial boundary value problem ∂u/∂t + Au = f in the assumption that finite difference analog A of the spatial differential operator A is representable as an M-matrix we present the stability analysis of so-called replicatively splitted schemes, i.e., two-layer schemes where difference operators on both time layers are amounting to the initial operator A and inherit its property (representability as M-matrix). For such schemes we give in the general form the stability sufficient condition in the norm ||z|| = max i |x i |. In the important special case the condition coincides with Neumann's necessary feature. The replicative splitting approach may naturally be extended on the ADI schemes, for example, here we also present the convergence sufficient condition to the Peaceman - Rachford's scheme for iterative solution of linear systems with non-symmetric M-matrix.