Asymptotic error expansion of two-dimensional Volterra integral equation by iterated collocation

摘要

In this paper, the numerical solution of two-dimensional linear Volterra integral equation by collocation and iterated collocation is considered. The asymptotic error expansion of the iterated collocation is obtained. We show that when piecewise polynomials of πp-1,q-1 are used, the iterated collocation solution admits an error expansion in powers of the step-size h and step-size k. For a special choice of the collocation point, the leading terms in the error expansion for iterated collocation contain only even powers of the stepsizes h and k, beginning with terms in h2p and k2q so that the Richardson extrapolation can be done. This will increase the accuracy of numerical solution greatly.