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Superconvergence of collocation methods for Volterra integral equations of the first kind

Superkonvergenz bei Kollokationsmethoden für Volterrasche Integralgleichungen erster Art

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Abstract

Collocation methods for solving first-kind Volterra equations in the space of piecewise polynomials possessing finite (jump) discontinuities at their knots and having degreem≧0 are known to have global order of convergencep=m+1. It is shown that a careful choice of the collocation points (characterized by the Lobatto points in (0, 1]) yields convergence of order (m+2) at the corresponding Legendre points.

Zusammenfassung

Wird eine Volterrasche Integralgleichung erster Art durch Kollokation im Raum der stückweisen Polynome vom Gradm≧0, welche Sprungstellen an den Knoten besitzen, gelöst, so ist die globale Konvergenzordnung der Näherungslösung durchp=m+1 gegeben. In dieser Arbeit wird gezeigt, daß eine spezielle Wahl der Kollokationspunkte (charakterisiert durch die Lobatto-Abszissen in (0, 1]) eine um Eins höhere Konvergenzordnung an den entsprechenden Legendre-Abszissen liefert.

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References

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Authors and Affiliations

  1. Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada

    H. Brunner

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  1. H. Brunner
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Additional information

This research was supported by the National Research Council of Canada (Grant A-4805).

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Brunner, H. Superconvergence of collocation methods for Volterra integral equations of the first kind. Computing 21, 151–157 (1979). https://doi.org/10.1007/BF02253135

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  • DOI: https://doi.org/10.1007/BF02253135

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