Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind

In this paper, we propose a suitable combination of two different Nyström methods, both using the zeros of the same sequence of Jacobi polynomials, in order to approximate the solution of Fredholm integral equations on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&quo...

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Autores principales:	Domenico Mezzanotte, Donatella Occorsio, Maria Grazia Russo
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Fredholm integral equations Nyström methods product integration rules orthogonal polynomials Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a0e58cc1d0ab4268854583e635739de8
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spelling	oai:doaj.org-article:a0e58cc1d0ab4268854583e635739de82021-11-11T18:13:49ZCombining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind10.3390/math92126522227-7390https://doaj.org/article/a0e58cc1d0ab4268854583e635739de82021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2652https://doaj.org/toc/2227-7390In this paper, we propose a suitable combination of two different Nyström methods, both using the zeros of the same sequence of Jacobi polynomials, in order to approximate the solution of Fredholm integral equations on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>. The proposed procedure is cheaper than the Nyström scheme based on using only one of the described methods . Moreover, we can successfully manage functions with possible algebraic singularities at the endpoints and kernels with different pathologies. The error of the method is comparable with that of the best polynomial approximation in suitable spaces of functions, equipped with the weighted uniform norm. The convergence and the stability of the method are proved, and some numerical tests that confirm the theoretical estimates are given.Domenico MezzanotteDonatella OccorsioMaria Grazia RussoMDPI AGarticleFredholm integral equationsNyström methodsproduct integration rulesorthogonal polynomialsMathematicsQA1-939ENMathematics, Vol 9, Iss 2652, p 2652 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Fredholm integral equations Nyström methods product integration rules orthogonal polynomials Mathematics QA1-939
spellingShingle	Fredholm integral equations Nyström methods product integration rules orthogonal polynomials Mathematics QA1-939 Domenico Mezzanotte Donatella Occorsio Maria Grazia Russo Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
description	In this paper, we propose a suitable combination of two different Nyström methods, both using the zeros of the same sequence of Jacobi polynomials, in order to approximate the solution of Fredholm integral equations on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>. The proposed procedure is cheaper than the Nyström scheme based on using only one of the described methods . Moreover, we can successfully manage functions with possible algebraic singularities at the endpoints and kernels with different pathologies. The error of the method is comparable with that of the best polynomial approximation in suitable spaces of functions, equipped with the weighted uniform norm. The convergence and the stability of the method are proved, and some numerical tests that confirm the theoretical estimates are given.
format	article
author	Domenico Mezzanotte Donatella Occorsio Maria Grazia Russo
author_facet	Domenico Mezzanotte Donatella Occorsio Maria Grazia Russo
author_sort	Domenico Mezzanotte
title	Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
title_short	Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
title_full	Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
title_fullStr	Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
title_full_unstemmed	Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind
title_sort	combining nyström methods for a fast solution of fredholm integral equations of the second kind
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a0e58cc1d0ab4268854583e635739de8
work_keys_str_mv	AT domenicomezzanotte combiningnystrommethodsforafastsolutionoffredholmintegralequationsofthesecondkind AT donatellaoccorsio combiningnystrommethodsforafastsolutionoffredholmintegralequationsofthesecondkind AT mariagraziarusso combiningnystrommethodsforafastsolutionoffredholmintegralequationsofthesecondkind
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Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind

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