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

Authors:
Jingtang Ma;Yingjun Jiang
Affiliations:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China;Department of Mathematics and Scientific Computing, Changsha University of Science and Technology, Changsha, 410076, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 5
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Abstract

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.