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.
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