Asymptotic error expansion of two-dimensional Volterra integral equation by iterated collocation (Q1322901)

The authors study the numerical solution of two-dimensional linear Volterra integral equations. Collocation and iterated collocation methods are discussed. An asymptotic error expansion for the iterated collocation solution is given. When piecewise polynomials are used, the iterated collocation solution admits an error expansion in powers of the step- sizes in the two-dimensions. For a special choice of the collocation points, the leading terms in the error expansion are of even order in the step-sizes, so that Richardson extrapolation can be done.