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Zbl 0634.65142
Brunner, Hermann
Polynomial spline collocation methods for Volterra integrodifferential equations with weakly singular kernels. (English)
[J] IMA J. Numer. Anal. 6, 221-239 (1986). ISSN 0272-4979; ISSN 1464-3642/e

Author's summary: We investigate the attainable order of (global) convergence of collocation approximations in certain polynomial spline spaces for the solution of Volterra integrodifferential equations with weakly singular kernels. While the use of quasi-uniform meshes leads, due to the nonsmooth nature of these solutions, to convergence of order less than one, regardless of the degree of the approximating spline function, collocation on suitably graded meshes will be shown to yield optimal convergence rates.
[Z.Jackiewicz]

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations

Keywords: order of (global) convergence; collocation; polynomial spline; Volterra integrodifferential equations; weakly singular kernels; quasi-uniform meshes; optimal convergence rates

Cited in: Zbl 0765.65126

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