Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments Original Research Article

In this paper we give a complete analysis of convergence acceleration method for discrete collocation solutions of Volterra integral equations with constant delay. It will be shown that, when continuous piecewise polynomials of degree m≤2 are used, and collocation is based on the Lobatto points, this discrete collocation approximation admits, at the knots, an error expansion in even powers of the step-size h, beginning with a term in h2m. Based on this expansion we show that, when a correction procedure is applied to such discrete collocation approximation for k times, the global accuracy of the corresponding corrected approximation will be increased to View the MathML source.