On the numerical solution of delay differential equations.

Abstract

A numerical method for the treatment of non-vanishing lag state dependent delay differential equations is developed in this work. This method is based on a (5,6) Runge-Kutta formula pair. The delayed term is approximated by a three-point Hermite polynomial. In order to obtain a highly accurate numerical scheme, special attention is given to the characterization and the localization of the derivative jump discontinuities of the solution. Some real-life problems are used to test the new method and compare it with existing ones.