Dissipativity of Runge–Kutta methods for Volterra functional differential equations

This paper is concerned with the numerical dissipativity of nonlinear Volterra functional differential equations (VFDEs). We give some dissipativity results of Runge–Kutta methods when they are applied to VFDEs. These results provide unified theoretical foundation for the numerical dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. Numerical examples are given to confirm our theoretical results.