Stepsize control for delay differential equations using continuously imbedded runge–kutta methods of sarafyan

摘要

The use of continuously imbedded Runge–Kutta–Sarafyan methods for the solution of ordinary differential equations with either time-dependent or state-dependent delays is discussed. It is shown how to get reliable solutions for such problems in a manner that does not require that the effect of the local approximation error be considered separately from the local integration error. It is also shown how to reliably handle derivative discontinuities that arise in the solution of differential equations with delays.