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Solving nonlinear functional-differential and functional equations with constant delay via block boundary value methods. (English) Zbl 07316756

Summary: This paper deals with the numerical solutions of nonlinear functional-differential and functional equations (FDFEs) with constant delay. The block boundary value methods (BBVMs) are extended to solve the FDFEs. Under the suitable conditions, it is shown that the extended BBVMs are uniquely solvable and globally stable. Moreover, the method can be convergent of order \(p\) whenever the Lipschitz condition holds and this method is preconsistent and \(p\)-order consistent. With several numerical examples, the theoretical results and computational validity of the extended BBVMs are further confirmed.

MSC:

34Hxx Control problems involving ordinary differential equations
49-XX Calculus of variations and optimal control; optimization
34Kxx Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
49Jxx Existence theories in calculus of variations and optimal control
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