Abstract
A method for the numerical solution of initial value problems for systems of retarded delay-differential equations is described. It uses a variable step Runge-Kutta Fehlberg 4/5 method combined with fourth degree Hermite-Birkhoff interpolation, which makes the usual local error estimator asymptotically correct. To obtain good numerical stability, the basic interpolation is modified for small delays. The possible initial discontinuities are algorithmically treated by using a very short stepsize in the critical step, and to this end the stepsize control has been somewhat modified. Numerical examples are included.
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Oppelstrup, J. (1978). The RKFHB4 method for delay — Differential equations. In: Bulirsch, R., Grigorieff, R.D., Schröder, J. (eds) Numerical Treatment of Differential Equations. Lecture Notes in Mathematics, vol 631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067469
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DOI: https://doi.org/10.1007/BFb0067469
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