A type insensitive code for delay differential equations basing on adaptive and explicit Runge-Kutta interpolation methods

For the numerical solution of initial value problems for delay differential equations with constant delay a partitioned Runge-Kutta interpolation method is studied which integrates the whole system either as a stiff or as a nonstiff one in subintervals. This algorithm is based on an adaptive Runge-Kutta interpolation method for stiff delay equations and on an explicit Runge-Kutta interpolation method for nonstiff delay equations. The retarded argument is approximated by appropriate Lagrange or Hermite interpolation. The algorithm takes advantage of the knowledge of the first points of jump discontinuities. An automatic stiffness detection and a stepsize control are presented. Finally, numerical tests and comparisons with other methods are made on a great number of problems including real-life problems.