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Der Einfluß von Randsingularitäten beim Ritzschen Verfahren

Sollution effects of the ritz method

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Summary

Discussed is the Ritz-method for a Sturm-Liouville problem with one singular boundary point. It is shown that the error locally admits the expansion

$$\omega (r) = \frac{{r^2 }}{{2(r^2 + d)^{1/2} }}$$

withn being the degree of the spline subspaces used.y 2 is a special solution of the homogeneous differential equation. Depending on the data ϰ h may be of orderh 1+ε with ε>0 arbitrary small and ϰ h cannot be eliminated by extrapolation.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität, Hermann-Herder-Str. 10, D-7800, Freiburg, Bundesrepublik Deutschland

    J. A. Nitsche

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  1. J. A. Nitsche
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Die Arbeit entstand während eines Gastaufenthalts am Mathematical Research Center, University of Madison, U.S.A.

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Nitsche, J.A. Der Einfluß von Randsingularitäten beim Ritzschen Verfahren. Numer. Math. 25, 263–278 (1975). https://doi.org/10.1007/BF01399415

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