Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations

Abstract

In this paper we deal with numerical solutions for a class of nonlinear second order delay differential equations. In order to approximate this problems, the block methods consisting of generalized Störmer-Cowell methods are proposed. The error analysis indicates, under appropriate conditions, the numerical schemes can have convergence of order p when they are consistent of order p. Finally, some numerical experiments are performed to illustrate accuracy of proposed methods and corresponding theoretical results.