SOFTWARE FOR THE NUMERICAL-SOLUTION OF SYSTEMS OF FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAYS

The theoretical basis for the numerical solution of a general class of functional differential equations is reviewed. A software package for the solution of differential equations with state-dependent delays is discussed. The package uses continuously imbedded Runge-Kutta methods of Sarafyan. These methods are based on C1 piecewise polynomial interpolants which are used to handle tasks associated with root finding and interpolation. In addition to providing a means to handle user-defined root finding requirements, they provide a means to locate automatically derivative discontinuities that arise in the solution of differential equations with delays. Examples are presented which demonstrate the manner in which the software takes into account the pertinent theoretical characteristics of functional differential equations.