Spectral approximation methods for nonlinear integral equations with non-smooth kernels
Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre poly...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Allouch, C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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© The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Calcolo - Springer International Publishing, 1964, 60(2023), 2 vom: 23. Apr. |
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| Übergeordnetes Werk: |
volume:60 ; year:2023 ; number:2 ; day:23 ; month:04 |
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| DOI / URN: |
10.1007/s10092-023-00519-3 |
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| 520 | |a Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. | ||
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| 700 | 1 | |a Tahrichi, M. |4 aut | |
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10.1007/s10092-023-00519-3 doi (DE-627)OLC2144106487 (DE-He213)s10092-023-00519-3-p DE-627 ger DE-627 rakwb eng 510 VZ Allouch, C. verfasserin aut Spectral approximation methods for nonlinear integral equations with non-smooth kernels 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. integral equation Orthogonal projection Interpolatory projection Polynomial Superconvergence Sbibih, D. aut Tahrichi, M. aut Enthalten in Calcolo Springer International Publishing, 1964 60(2023), 2 vom: 23. Apr. (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:60 year:2023 number:2 day:23 month:04 https://doi.org/10.1007/s10092-023-00519-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 60 2023 2 23 04 |
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10.1007/s10092-023-00519-3 doi (DE-627)OLC2144106487 (DE-He213)s10092-023-00519-3-p DE-627 ger DE-627 rakwb eng 510 VZ Allouch, C. verfasserin aut Spectral approximation methods for nonlinear integral equations with non-smooth kernels 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. integral equation Orthogonal projection Interpolatory projection Polynomial Superconvergence Sbibih, D. aut Tahrichi, M. aut Enthalten in Calcolo Springer International Publishing, 1964 60(2023), 2 vom: 23. Apr. (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:60 year:2023 number:2 day:23 month:04 https://doi.org/10.1007/s10092-023-00519-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 60 2023 2 23 04 |
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10.1007/s10092-023-00519-3 doi (DE-627)OLC2144106487 (DE-He213)s10092-023-00519-3-p DE-627 ger DE-627 rakwb eng 510 VZ Allouch, C. verfasserin aut Spectral approximation methods for nonlinear integral equations with non-smooth kernels 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. integral equation Orthogonal projection Interpolatory projection Polynomial Superconvergence Sbibih, D. aut Tahrichi, M. aut Enthalten in Calcolo Springer International Publishing, 1964 60(2023), 2 vom: 23. Apr. (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:60 year:2023 number:2 day:23 month:04 https://doi.org/10.1007/s10092-023-00519-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 60 2023 2 23 04 |
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10.1007/s10092-023-00519-3 doi (DE-627)OLC2144106487 (DE-He213)s10092-023-00519-3-p DE-627 ger DE-627 rakwb eng 510 VZ Allouch, C. verfasserin aut Spectral approximation methods for nonlinear integral equations with non-smooth kernels 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. integral equation Orthogonal projection Interpolatory projection Polynomial Superconvergence Sbibih, D. aut Tahrichi, M. aut Enthalten in Calcolo Springer International Publishing, 1964 60(2023), 2 vom: 23. Apr. (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:60 year:2023 number:2 day:23 month:04 https://doi.org/10.1007/s10092-023-00519-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 60 2023 2 23 04 |
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10.1007/s10092-023-00519-3 doi (DE-627)OLC2144106487 (DE-He213)s10092-023-00519-3-p DE-627 ger DE-627 rakwb eng 510 VZ Allouch, C. verfasserin aut Spectral approximation methods for nonlinear integral equations with non-smooth kernels 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. integral equation Orthogonal projection Interpolatory projection Polynomial Superconvergence Sbibih, D. aut Tahrichi, M. aut Enthalten in Calcolo Springer International Publishing, 1964 60(2023), 2 vom: 23. Apr. (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:60 year:2023 number:2 day:23 month:04 https://doi.org/10.1007/s10092-023-00519-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 60 2023 2 23 04 |
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Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. A numerical example is given to illustrate the theoretical results. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2144106487</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240118093333.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">240118s2023 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10092-023-00519-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2144106487</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10092-023-00519-3-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Allouch, C.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Spectral approximation methods for nonlinear integral equations with non-smooth kernels</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, polynomially based projection and modified projection methods for approximating the solution of Uryshon integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and the superconvergence of their iterated versions are analyzed. 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