In this paper we introduce a measure for calculating statistically significant collocation sets that is related to the Poisson distribution. We show that results calculated using this measure are comparable to well-known measures like the log-likelihood measure. Additionally, we discuss asymptotic behaviour and additivity as general properties of the measure which may be applied to the analysis...

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [14] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also disc...

A Multistep collocation techniques is used in this paper to develop a 3-point explicit and implicit block methods, which are suitable for generating solutions of the general second-order ordinary differential equations of the form y′′ f x, y, y′ , y x0 a, y′ x0 b. The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The Stability and Conv...

This document discusses accuracy of the collocation technique we employ to calculate the velocity field in ambient inviscid fluid above an interface swollen by a denser source fluid.

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). We outline how Fourier and Laplace transforms can be used to obtain an O(h) convergence result for a “polar” piecewise–linear collocation approximation of a scalar RPIE on an infinite flat plate.