Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods

摘要

A variable-stepsize one-step collocation method for solving general nonlinear second kind Volterra integral equations is presented. The iterated collocation method corresponding to polynomial spline collocation is extended to nonlinear Volterra integral equations of the second kind. The resulting superconvergence properties of the collocation approximation or the iterated collocation approximation are used to obtain (local and global) error estimates which in turn form the basis of a variable stepsize code. The performance of this code is illustrated by test problems.