The extended block generalized Störmer–Cowell methods for second-order nonlinear delay-differential–algebraic equations with index-1

Abstract

This paper is concerned with the numerical solutions of second-order nonlinear delay-differential–algebraic equations (SNDDAEs) with index-1. By extending block generalized Störmer–Cowell methods (BGSCMs) for second-order ordinary differential equations, a class of efficient numerical algorithms for solving index-1 SNDDAEs are derived. It is proved that the extended BGSCMs are uniquely solvable and convergent of order p, where p is the consistence order of the methods. Numerical example is presented to illustrate the computational effectiveness of the extended BGSCMs and the correctness of the corresponding theoretical results.