A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel

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Abstract

This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. Owing to I he singular behavior of the solution near the origin, the global convergence order of product integration and collocation methods is not optimal. In order to recover the optimal orders a hybrid collocation method is used which combines a non-polynomial approximation on the first subinterval followed by piecewise polynomial collocation on a graded mesh. Some numerical examples are presented which illustrate the theoretical results and the performance of the method. A comparison is made with the standard graded collocation method. (C) 2010 Elsevier B.V. All rights reserved.
Original languageUnknown
Pages (from-to)2859-2869
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number9
DOIs
Publication statusPublished - 1 Jan 2010

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