DKLAG6: A Code Based on Continuously Imbedded Sixth Order Runge{Kutta Methods for the Solution of State Dependent Functional Di erential Equations

This paper discusses a new family of sixth{order continuously imbedded Runge{Kutta{ Sarafyan methods and a mathematical software package DKLAG6 for the numerical solution of systems of functional di erential equations with state dependent delays. The methods used are based on piecewise polynomial approximants which are used for error estimation and stepsize selection, to handle the necessary interpolations for delayed solution values, to handle the root nding associated with locating the delay{induced points of derivative discontinuity, and to perform other root nding tasks in a manner similar to other well{known root nding ordinary and delay di erential equation solvers. DKLAG6 is applicable to problems with vanishing and nearly vanishing delays and may be used for neutral systems containing delayed derivatives. Basic features of DKLAG6 are summarized and its typical performance is illustrated using examples with di erent types of delays. Comparative test results are given for DKLAG6 and its predecessor DKLAG5 which is based on fourth and fth order continuously imbedded Runge{Kutta{Sarafyan methods.