Volume 6, Number 3, Fall 1998
COLLOCATION APPROXIMATIONS FOR SECOND-ORDER
DIFFERENTIAL EQUATIONS AND VOLTERRA
WITH VARIABLE DELAYS
WENKUI ZHANG AND HERMANN BRUNNER
Abstract. In this paper we analyze the convergence
properties of m-stage implicit (collocation-based) Runge-Kutta
methods for second-order differential equations and Volterra
integro-differential equations with variable delay qt, 0 < q < 1.
A discussion of local superconvergence and numerical illustrations
are also given.