Computer solutions of state-dependent delay differential equations

Abstract

An adaptation of the Runge-Kutta-Verner (5, 6) formula pair is used to construct a numerical method for the solution of state-dependent delay differential equations with nonvanishing lag. A fifth-degree divided-difference Newton backward interpolation polynomial is used to find the location of the derivative jump discontinuities of the solution. In order to maintain the sixth-order accuracy of the RKV pair, the value of the solution at the delay is approximated by a three-point Hermite polynomial. This new method is tested on some real-life problems. A Fortran program, called SYSDEL, is available from the authors.