The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes

Author:
Hermann Brunner

Journal:
Math. Comp. **45** (1985), 417-437

MSC:
Primary 65R20; Secondary 45D05

DOI:
https://doi.org/10.1090/S0025-5718-1985-0804933-3

MathSciNet review:
804933

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Abstract: 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0804933-3

Keywords:
Volterra integral equations,
weakly singular kernels,
polynomial spline collocation,
graded meshes

Article copyright:
© Copyright 1985
American Mathematical Society