Using Operator Inequalities in Studying the Stability of Difference Schemes for Nonlinear Boundary Value Problems with Nonlinearities of Unbounded Growth
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引用次数: 0
Abstract
The article develops the theory of stability of linear operator schemes for operator
inequalities and nonlinear nonstationary initial–boundary value problems of mathematical physics
with nonlinearities of unbounded growth. Based on sufficient conditions for the stability of
A.A. Samarskii’s two- and three-level difference schemes, the corresponding a priori estimates for
operator inequalities are obtained under the condition of the criticality of the difference schemes
under consideration, i.e., when the difference solution and its first time derivative are nonnegative
at all nodes of the grid domain. The results obtained are applied to the analysis of the stability of
difference schemes that approximate the Fisher and Klein–Gordon equations with nonlinear
right-hand sides.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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