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High order projection methods of moment- and collocation-type for nonlinear boundary value problems

Hochkonvergente Projektionsmethoden vom Momenten- und Kollokationstyp für nichtlineare Randwertaufgaben

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Abstract

Approximations to an isolated solution of a two point boundary value problem are determined by projection methods with piecewise polynomial functions. Some principles are derived which lead in a uniform way to statements of high-order convergence for a variety of moment-type methods and collocation methods with Gaussian nodes.

Zusammenfassung

Näherungen für eine isolierte Lösung einer Zweipunkt-Randwertaufgabe werden durch Projektionsmethoden mit stückweise polynomischen Funktionen ermittelt. Einige Überlegungen prinzipieller Art führen in einheitlicher Weise zu Aussagen über hohe Konvergenzordnung für eine Vielzahl von Momentenmethoden und Kollokationsmethoden mit Gaußschen Knoten.

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References

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Authors and Affiliations

  1. Institut für Angewandte Mathematik Technische Hochschule München, Arcisstraße 21, D-8000, München, Bundesrepublik Deutschland

    K. A. Wittenbrink

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  1. K. A. Wittenbrink
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Additional information

This paper is in part an extension of the author's dissertation [8].

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Wittenbrink, K.A. High order projection methods of moment- and collocation-type for nonlinear boundary value problems. Computing 11, 255–274 (1973). https://doi.org/10.1007/BF02252915

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  • DOI: https://doi.org/10.1007/BF02252915

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