On a Maximum Principle for Matrices, and on Conservation of Monotonicity. With Applications to Discretization Methods
Gisbert Stoyan · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1982
Abstract Considered are two kinds of monotonicity properties of systems of linear equations. Firstly, a maximum principle is defined for matrices of monotone kind, and sufficient conditions are given for its validity. Secondly, for more special systems, sufficient conditions are established under which (componentwise) monotonicity of the right‐hand side implies monotonicity of the solution. A series of examples is considered for the investigated concepts, mainly from the context of difference schemes, leading to some new results for well‐known schemes.