Abstract
In a previous paper the Kupradze functional equation has been investigated with respect to uniqueness, and it was found necessary to replace the Kupradze equation by a pair of equations. Here we consider the numerical implementation of the pair of equations, and we show how the pair may be treated in order to obtain a satisfactory numerical solution. We also consider the effect of the quadrature error on the solution, whereby we get numerical reasons for a modification of the pair of equations. A major part of the investigation is based on matrix condition numbers formed from the singular values of the matrices.
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Christiansen, S. (1980). Numerical Treatment of an Integral Equation Originating from a Two-Dimensional Dirichlet Boundary Value Problem. In: Albrecht, J., Collatz, L. (eds) Numerical Treatment of Integral Equations / Numerische Behandlung von Integralgleichungen. International Series of Numerical Mathematics / International Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6314-8_5
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DOI: https://doi.org/10.1007/978-3-0348-6314-8_5
Publisher Name: Birkhäuser, Basel
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