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

Authors:
Magda Rebelo;Teresa Diogo
Affiliations:
Departamento de Matemática, Faculdade de Ciências e Tecnologia, Monte da Caparica, 2829-516 Caparica, Portugal;CEMAT-Departamento de Matemática, Instituto Superior Técnico/UTL, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 2
Cited 2

The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations

Mathematics of Computation
A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels

SIAM Journal on Numerical Analysis

A Nyström interpolant for some weakly singular nonlinear Volterra integral equations

Journal of Computational and Applied Mathematics
Fully discretized collocation methods for nonlinear singular Volterra integral equations

Journal of Computational and Applied Mathematics

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Abstract

This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. Owing to the 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.