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Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations

Vergleich von numerischen Quadraturformeln für schwach singuläre periodische Fredholm-Integralgleichungen

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Abstract

Several numerical quadrature formulas that are used in the quadrature method for the numerical solution of periodic Fredholm integral equations are analyzed and precise asymptotic expansions for their errors are derived. All of these formulas are based on the trapezoidal rule with equidistant abscissas. They are compared with respect to their computational cost, accuracy, and efficiency when used in conjunction with the Richardson extrapolation. On the basis of this comparison it is concluded that the formula developed in [4] is the most advantageous. A numerical example is appended.

Zusammenfassung

Eine Reihe numerischer Quadraturformeln, die bei der numerischen Lösung periodischer Fredholm-Integralgleichungen in Verwendung sind, werden analysiert und es werden für ihre Fehler genaue asymetrische Entwicklungen hergeleitet. Alle diese Formeln beruhen auf der Trapezregel mit gleichabständigen Abszissen. Sie werden bezüglich Rechenaufwand, Genauigkeit und Effizienz bei Ihrer Verwendung im Zusammenhang mit Richardson-Extrapolation verglichen. Es ergibt sich, daß die Formel aus [4] am vorteilhaftesten ist. Ein numerisches Beispiel ist beigefügt.

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References

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Authors and Affiliations

  1. Computer Science Department, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Avram Sidi

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  1. Avram Sidi
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Sidi, A. Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations. Computing 43, 159–170 (1989). https://doi.org/10.1007/BF02241859

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  • DOI: https://doi.org/10.1007/BF02241859

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