Classical theory of Runge–Kutta methods for Volterra functional differential equations

For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are established. The methods studied and the theories established in this paper can be directly applied to non-stiff non-linear initial value problems in delay differential equations (DDEs), integro-differential equations (IDEs), delay integro-differential equations (DIDEs), and VFDEs of other type which appear in practice, and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff VFDEs.