Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation
Abstract This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gupta, Reema [verfasserIn] Chakraverty, Snehashish [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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: Methodology and computing in applied probability - Springer US, 1999, 26(2024), 4 vom: 05. Okt. |
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| Übergeordnetes Werk: |
volume:26 ; year:2024 ; number:4 ; day:05 ; month:10 |
| Links: |
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| DOI / URN: |
10.1007/s11009-024-10114-w |
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| Katalog-ID: |
SPR057684286 |
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| 520 | |a Abstract This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. | ||
| 650 | 4 | |a Stochastic integral equation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Brownian motion |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Vieta-Fibonacci polynomials |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stability analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Convergence analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Pseudo-Spectral Galerkin method |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Chakraverty, Snehashish |e verfasserin |4 aut | |
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10.1007/s11009-024-10114-w doi (DE-627)SPR057684286 (SPR)s11009-024-10114-w-e DE-627 ger DE-627 rakwb eng 004 VZ 31.70 bkl 31.80 bkl Gupta, Reema verfasserin aut Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 Chakraverty, Snehashish verfasserin aut Enthalten in Methodology and computing in applied probability Springer US, 1999 26(2024), 4 vom: 05. Okt. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:26 year:2024 number:4 day:05 month:10 https://dx.doi.org/10.1007/s11009-024-10114-w X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 VZ 31.80 VZ AR 26 2024 4 05 10 |
| spelling |
10.1007/s11009-024-10114-w doi (DE-627)SPR057684286 (SPR)s11009-024-10114-w-e DE-627 ger DE-627 rakwb eng 004 VZ 31.70 bkl 31.80 bkl Gupta, Reema verfasserin aut Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 Chakraverty, Snehashish verfasserin aut Enthalten in Methodology and computing in applied probability Springer US, 1999 26(2024), 4 vom: 05. Okt. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:26 year:2024 number:4 day:05 month:10 https://dx.doi.org/10.1007/s11009-024-10114-w X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 VZ 31.80 VZ AR 26 2024 4 05 10 |
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10.1007/s11009-024-10114-w doi (DE-627)SPR057684286 (SPR)s11009-024-10114-w-e DE-627 ger DE-627 rakwb eng 004 VZ 31.70 bkl 31.80 bkl Gupta, Reema verfasserin aut Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 Chakraverty, Snehashish verfasserin aut Enthalten in Methodology and computing in applied probability Springer US, 1999 26(2024), 4 vom: 05. Okt. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:26 year:2024 number:4 day:05 month:10 https://dx.doi.org/10.1007/s11009-024-10114-w X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 VZ 31.80 VZ AR 26 2024 4 05 10 |
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10.1007/s11009-024-10114-w doi (DE-627)SPR057684286 (SPR)s11009-024-10114-w-e DE-627 ger DE-627 rakwb eng 004 VZ 31.70 bkl 31.80 bkl Gupta, Reema verfasserin aut Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 Chakraverty, Snehashish verfasserin aut Enthalten in Methodology and computing in applied probability Springer US, 1999 26(2024), 4 vom: 05. Okt. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:26 year:2024 number:4 day:05 month:10 https://dx.doi.org/10.1007/s11009-024-10114-w X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 VZ 31.80 VZ AR 26 2024 4 05 10 |
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10.1007/s11009-024-10114-w doi (DE-627)SPR057684286 (SPR)s11009-024-10114-w-e DE-627 ger DE-627 rakwb eng 004 VZ 31.70 bkl 31.80 bkl Gupta, Reema verfasserin aut Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 Chakraverty, Snehashish verfasserin aut Enthalten in Methodology and computing in applied probability Springer US, 1999 26(2024), 4 vom: 05. Okt. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:26 year:2024 number:4 day:05 month:10 https://dx.doi.org/10.1007/s11009-024-10114-w X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 VZ 31.80 VZ AR 26 2024 4 05 10 |
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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 This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. 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004 VZ 31.70 bkl 31.80 bkl Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation Stochastic integral equation (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Vieta-Fibonacci polynomials (dpeaa)DE-He213 Stability analysis (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Pseudo-Spectral Galerkin method (dpeaa)DE-He213 |
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pseudo-spectral galerkin method using shifted vieta-fibonacci polynomials for stochastic models: existence, stability, and numerical validation |
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Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation |
| abstract |
Abstract This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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. |
| abstractGer |
Abstract This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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_unstemmed |
Abstract This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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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Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation |
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Chakraverty, Snehashish |
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|
| score |
7.400012 |