DKLAG6: a code based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent functional differential 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 differential 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 rootfinding associated with locating the delay-induced points of derivative discontinuity, and to perform other rootfinding tasks in a manner similar to other well-known rootfinding ordinary and delay differential 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 different types of delays. Comparative test results are given for DKLAG6 and its predecessor DIUAGS which is based on fourthand fifth-order continuously imbedded Runge-Kutta-Sarafyan methods.