$B$-Convergence Theory of Runge--Kutta Methods for Stiff Volterra Functional Differential Equations with Infinite Integration Interval

In this paper, $B$-convergence theory of Runge--Kutta methods for nonlinear stiff Volterra functional differential equations is extended from finite integration interval $[a,T]$ to infinite integration interval $[a,+\infty)$. The results obtained are of importance for the study of functional differential dynamic systems and for long time stiff computation.