Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order Delay-Integro-Differential Equations

Abstract

This paper deals with the numerical solutions of nonlinear boundary value problems (BVPs) of second-order delay-integro-differential equations. The generalized Stormer–Cowell methods (GSCMs), combined with the compound quadrature rules, are extended to solve this class of BVPs. It is proved under some suitable conditions that the extended GSCMs are uniquely solvable, stable and convergent of order $$\min \{p,q\}$$ , where p, q are consistent order of the GSCMs and convergent order of the compound quadrature rules, respectively. Several numerical examples are presented to illustrate the proposed methods and their theoretical results. Moreover, a numerical comparison with the existed methods is also given, which shows that the extended GSCMs are comparable in numerical precision and computational cost.