Some considerations on numerical methods for Cauchy singular integral equations on the real line
Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.
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| Published in | Mathematical modelling and analysis Vol. 29; no. 2; pp. 268 - 276 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Vilnius
Vilnius Gediminas Technical University
26.03.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1392-6292 1648-3510 1648-3510 |
| DOI | 10.3846/mma.2024.18688 |
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| Abstract | Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation. |
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| AbstractList | Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation. Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation. Keywords: Hilbert transform, singular integral equation, Hermite weight. AMS Subject Classification: 45E05; 47B38. |
| Audience | Academic |
| Author | Capobianco, Maria Rosaria Criscuolo, Giuliana |
| Author_xml | – sequence: 1 givenname: Maria Rosaria surname: Capobianco fullname: Capobianco, Maria Rosaria organization: Istituto per le Applicazioni del Calcolo “M. Picone” - C.N.R. Sede di Napoli, Via Pietro Castellino 111, 80131 Napoli, Italy – sequence: 2 givenname: Giuliana surname: Criscuolo fullname: Criscuolo, Giuliana organization: Dipartimento di Matematica e Applicazioni, Universit´a degli Studi di Napoli “Federico II”, Complesso Monte Sant’Angelo, Edificio T, Via Cintia, 80126 Napoli, Italy |
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| Copyright | Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University. COPYRIGHT 2024 Vilnius Gediminas Technical University 2024. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| SubjectTerms | Analysis Approximation Cauchy problem Hermite weight Hilbert transform Integral equations Mathematical analysis Methods Numerical analysis Numerical methods Polynomials singular integral equation Singular integral equations Smoothness Tests, problems and exercises |
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| Title | Some considerations on numerical methods for Cauchy singular integral equations on the real line |
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