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Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

✍ Scribed by Teresa Diogo

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
590 KB
Volume
229
Category
Article
ISSN
0377-0427

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✦ Synopsis

We discuss the convergence properties of spline collocation and iterated collocation methods for a weakly singular Volterra integral equation associated with certain heat conduction problems. This work completes the previous studies of numerical methods for this type of equations with noncompact kernel. In particular, a global convergence result is obtained and it is shown that discrete superconvergence can be achieved with the iterated collocation if the exact solution belongs to some appropriate spaces. Some numerical examples illustrate the theoretical results.

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In this paper we propose new numerical methods for linear Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equatio