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Newton methods for a class of nonlinear hypersingular integral equations |
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| Authors: | Maria Rosaria Capobianco Giuliana Criscuolo Peter Junghanns |
| Institution: | 1. Istituto per le Applicazioni del Calcolo “Mauro Picone”—CNR, Sezione di Napoli, Via Pietro Castellino 111, 80131, Napoli, Italy 2. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte Sant’Angelo, Edificio T, Via Cintia, 80126, Napoli, Italy 3. Fakult?t für Mathematik, Technische Universit?t Chemnitz, Reichenhainer Str. 39, 09126, Chemnitz, Germany |
| Abstract: | Different iterative schemes based on collocation methods have been well studied and widely applied to the numerical solution of nonlinear hypersingular integral equations (Capobianco et al. 2005). In this paper we apply Newton’s method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl’s type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented to validate the theoretical results. |
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