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

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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.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4

    W.H. Enright & H. Hayashi

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  1. W.H. Enright
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  2. H. Hayashi
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Correspondence to H. Hayashi.

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Enright, W., Hayashi, H. A delay differential equation solver based on a continuous Runge–Kutta method with defect control. Numerical Algorithms 16, 349–364 (1997). https://doi.org/10.1023/A:1019107718128

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