NDLI: The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes

Content Provider	Scilit
Author	Brunner, Hermann
Copyright Year	1985
Description	Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the problem of how to select the quadrature formulas to obtain the fully discretized collocation equation.
Related Links	https://www.ams.org/mcom/1985-45-172/S0025-5718-1985-0804933-3/S0025-5718-1985-0804933-3.pdf
Ending Page	437
Page Count	21
Starting Page	417
ISSN	00255718
e-ISSN	10886842
DOI	10.2307/2008134
Journal	Mathematics of Computation
Issue Number	172
Volume Number	45
Language	English
Publisher	Duke University Press
Publisher Date	1985-10-01
Access Restriction	Open
Subject Keyword	Mathematical Physics Graded Meshes Volterra Weakly Singular Equation Collocation Convergence Unbounded
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory Computational Mathematics

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The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes