R-K formulae applied to Volterra equations with delay

摘要

We consider convergence and stability of a class of Runge-Kutta formulae, applied to a class of Volterra integral equations with fixed delay. Although derived from standard Runge-Kutta tableau, the formulae differ from those applied to classical Volterra integral equations. Consideration of the formulae is prompted by the search for highly stable formulae which have acceptable orders of convergence. The theory and numerical results presented establish the existence of acceptable Runge-Kutta formulae.