A delay differential equation solver based on a continuous Runge–Kutta method with defect control

A method is described, DDVERK, which implements this approach and justifies the strategies and heuristics that have been adopted and shows how the assumptions related to error control, stepsize control, and discontinuity detection can be efficiently realized for a particular sixth-order numerical method.

Abstract

We have recently developed a generic approach for solving neutral delay differential equations based on the use of a continuous Runge–Kutta formula with defect control and investigated its convergence properties. In this paper, we describe a method, DDVERK, which implements this approach and justify the strategies and heuristics that have been adopted. In particular we show how the assumptions related to error control, stepsize control, and discontinuity detection (required for convergence) can be efficiently realized for a particular sixth-order numerical method. Summaries of extensive testing are also reported.