On Discrete Maximum Principles for Linear Equation Systems and Monotonicity of Difference Schemes

Authors:
V. S. Borisov
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2002

Citing 0
Cited 3

On discrete maximum principles for nonlinear elliptic problems

Mathematics and Computers in Simulation
On Stability, Monotonicity, and Construction of Difference Schemes I: Theory

SIAM Journal on Scientific Computing
On stability of difference schemes. Central schemes for hyperbolic conservation laws with source terms

Applied Numerical Mathematics

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Abstract

Discrete maximum principles for linear equation systems are discussed. A novel maximum principle for linear difference schemes is established. Sufficient conditions for an arbitrary linear scheme to satisfy the maximum principle are provided. Easily verifiable sufficient as well as necessary and sufficient conditions of nonsingularity for a diagonally dominant matrix, be it reducible or irreducible, are derived. Necessary and sufficient conditions for the validity of the maximum principle for explicit difference schemes are developed. The notion of submonotonicity for linear difference schemes as well as the notions of linear monotonicity and linear submonotonicity for nonlinear difference schemes are introduced and associated criteria developed. The developed approaches are demonstrated by examples of known linear and nonlinear difference schemes associated, in general, with the numerical analysis of systems of partial differential equations.