Solving nonlinear functional-differential and functional equations with constant delay via block boundary value methods

摘要

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. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.