Abstract
We consider a pair of integral equations derived by Symm (1967) and Hsiao & MacCamy (1973) for use in various boundary value problems. We investigate the matrix which results when some collocation methods are applied to these equations. We find that thel 2-condition number of the matrix can be reduced by performing three minor modifications of the integral equations.
Zusammenfassung
Wir betrachten ein Paar von Integralgleichungen, das von Symm (1967) und Hsiao & MacCamy (1973) zur Verwendung in verschiedenen Randwertaufgaben hergeleitet worden ist. Wir untersuchen die Matrix, die entsteht, wenn bestimmte Kollokationsmethoden auf die Integralgleichungen angewandt werden. Wir finden, daß diel 2-Konditionszahl der Matrix verkleinert werden kann, wenn drei einfache Modifikationen der Integralgleichungen durchgeführt werden.
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A previous version of this investigation was presented very briefly 14 April 1982 at the Scientific Meeting of “Gesellschaft für Angewandte Mathematik und Mechanik” (GAMMM) held in Budapest, Hungary [12].
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Christiansen, S. Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning. Computing 34, 221–242 (1985). https://doi.org/10.1007/BF02253319
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DOI: https://doi.org/10.1007/BF02253319