Implicit Difference InequalitiesCorresponding to First-Order PartialDifferentialFunctional Equations

[摘要] We give a theorem on implicit difference functional inequalities generatedby mixed problems for nonlinear systems of first-order partialdifferential functional equations. We apply this result in the investigationsof the stability of difference methods. Classical solutions of mixedproblems are approximated in the paper by solutions of suitable implicitdifference schemes. The proof of the convergence of difference methodis based on comparison technique, and the result on difference functionalinequalities is used. Numerical examples are presented.

[学科分类] 应用数学