Collocation methods for second-order Volterra integro-differential equations (Q1106648)

For the numerical solution of the second-order Volterra integro- differential equation \[ y''(t)=f(t,y(t))+\int^{t}_{0}k(t,s,y(s))ds \] the authors consider collocation methods in certain polynomial spline spaces. They prove global convergence and local superconvergence of these methods, and they show their relation to implicit Runge-Kutta-Nyström methods.