Stepsize control for delay differential equations using ... - Science Direct
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Stepsize control for delay differential equations using ... - Science Direct
Abstract: The use of continuously imbedded Runge-Kutta-Sarafyan methods for the ... This paper is concerned with the solution of ordinary differential equations ... The above form of the delay problem includes the constant delay form .... satisfy the fourth-order Runge-Kutta order equations for each value of c, 0 < c
Journal of Computational and Applied Mathematics 31 (1990) 267-275 North-Holland
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Stepsize control for delay differential equations using continuously imbedded Runge-Kutta methods of Sarafyan * S. T H O M P S O N Department of Mathematics and Statistics, Radford University, Radford, VA 24142, USA Received 11 October 1989 Revised 7 December 1989
Abstract: 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.
This paper is concerned with the solution of ordinary differential equations which contain delays. The techniques discussed are applicable to the solution of ordinary differential equations with state-dependent delays: dy(t)
