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

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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.