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A remark on the numerical computation of improper integrals

Eine Bemerkung zur numerischen Behandlung uneigentlicher Integrale

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Abstract

In this note a transformation is given reducing improper integrals to integrals with smooth integrands. The transformation may be represented in terms of elementary functions and is easily applicable in connection with standard mathematical software for the numerical evaluation of integrals with smooth integrands.

Zusammenfassung

In dieser Arbeit wird eine Transformation beschrieben, die die meisten uneigentlichen Integrale über endlichen Intervallen in Integrale mit glatten Integranden überführt. Diese Transformation kann durch elementare Funktionen ausgedrückt werden und ist leicht in Verbindung mit Standardverfahren zur numerischen Auswertung von Integralen mit glatten Integranden anwendbar.

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References

  1. de Doncker, E., Piessens, R.: Algorithm 32. Automatic computation of integrals with singular integrand, over a finite or infinite range. Computing17, 265–279 (1976).

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  2. Murato, K., Iri, M.: Parameter timing and repeated application of the IMT-type transformation in numerical quadrature. Numer. Math.36, 347–363 (1982).

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  3. Robinson, J., de Doncker, E.: Algorithm 45. Automatic computation of improper integrals over a bounded or unbounded planar region. Computing27, 253–284 (1981).

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Yserentant, H. A remark on the numerical computation of improper integrals. Computing 30, 179–183 (1983). https://doi.org/10.1007/BF02280788

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