Error estimation and step size control for delay differential equation solvers based on continuously embedded Runge-Kutta-Sarafyan methods

This paper considers the use of continuously embedded Runge-Kutta-Sarafyan methods for the solution of delay differential equations. It discusses simple ways to improve the error estimation and step size selection strategies for delay solvers based on Sarafyan methods. Numerical results are given which demonstrate the manner in which these estimates improve the accuracy of the solvers in a natural way.