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Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels

BRUNNER, HERMANN

In: IMA Journal of Numerical Analysis, 1986, vol. 6, no. 2, p. 221-239

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    Titre
    • Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
    Auteur
    • BRUNNER, HERMANN. Institut de Mathématiques, Université de Fribourg, CH-1700 Fribourg, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • IMA Journal of Numerical Analysis, 1986, vol. 6, no. 2, p. 221-239. Oxford University Press
    Autre version électronique
    Classification
    • Mathématiques
    Mots clés
    Identifiant OAI-PMH
    • oai:doc.rero.ch:303931
    Summary
    In this paper we investigate the attainable order of (global) convergence of collocation approximations in certain polynomial spline spaces for 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