High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations

A contractivity theory of Runge-Kutta methods for stiff nonlinear Volterra functional differential equations (VFDEs) is established, by means of which a family of high order contractive Runge-Kutta methods for VFDEs are identified. The application of the general theory for stiff nonlinear VFDEs to the special cases of stiff nonlinear delay differential equations and delay integro-differential equations is also presented.