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Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

โœ Scribed by Tomoaki Okayama; Takayasu Matsuo; Masaaki Sugihara

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
566 KB
Volume
234
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

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 equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far.

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Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations
โœ Teresa Diogo ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 590 KB

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 ker