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On a graded mesh method for a class of weakly singular Volterra integral equations

✍ Scribed by Jingtang Ma; Yingjun Jiang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
435 KB
Volume
231
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper a class of weakly singular Volterra integral equations with an infinite set of solutions is investigated. Among the set of solutions only one particular solution is smooth and all others are singular at the origin. The numerical solution of this class of equations has been a difficult topic to analyze and has received much previous investigation. The aim of this paper is to improve the convergence rates by a graded mesh method. The convergence rates are proved and a variety of numerical examples are provided to support the theoretical findings.

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Collocation and iterated collocation met
Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations
✍ Teresa Diogo πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 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