Abstract
Quadrature rules for the approximate evaluation of derivatives of Cauchy principal value integrals (with respect to the free variable inside the integral) can be obtained by formal differentiations of the right sides of the corresponding quadrature rules (without derivatives). The justification of this method, under appropriate conditions, is presented in this short communication. The results of this short communication are also applicable to the numerical evaluation of a class of finite-part integrals and to the numerical solution of singular integrodifferential equations.
Zusammenfassung
Quadraturformeln für die approximative Berechnung der Ableitungen Cauchyscher Hauptwertintegrale (bezüglich der freien Variablen der Integrale) können durch formale Differentiationen der rechten Seiten der verwendeten Integrationsformeln (ohne Ableitungen) genommen werden. Die Rechtfertigung dieser Methode unter geeigneten Bedingungen erscheint in dieser kurzen Mitteilung. Die Ergebnisse dieser kurzen Mitteilung sind auch anwendbar für die numerische Berechnung der endlichen Bestandteile gewisser divergenter Integrale und für die numerische Lösung singulärer Integrodifferentialgleichungen.
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Ioakimidis, N.I. On the numerical evaluation of derivatives of Cauchy principal value integrals. Computing 27, 81–88 (1981). https://doi.org/10.1007/BF02243440
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DOI: https://doi.org/10.1007/BF02243440