Fully discretized collocation methods for nonlinear singular Volterra integral equations

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Abstract

We consider a nonlinear weakly singular Volterra integral equation arising from a problem studied by Lighthill (1950) [1]. A series expansion for the solution is obtained and shown to be convergent in a neighbourhood of the origin. Owing to the singularity of the solution at the origin, the global convergence order of product integration and collocation methods is not optimal. However, the optimal orders can be recovered if we use the fully discretized collocation methods based on graded meshes. A theoretical proof is given and we present some numerical results which illustrate the performance of the methods.
Original languageUnknown
Pages (from-to)84-101
JournalJournal of Computational and Applied Mathematics
Volume247
Issue numberNA
DOIs
Publication statusPublished - 1 Jan 2013

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