Academic Journal
Orthogonal polynomial-based neural network solution for differential equations with implicit boundary conditions.
| Τίτλος: | Orthogonal polynomial-based neural network solution for differential equations with implicit boundary conditions. |
|---|---|
| Συγγραφείς: | Dey, Shilpa, Dubey, Shruti |
| Πηγή: | International Journal of Numerical Methods for Heat & Fluid Flow; 2025, Vol. 35 Issue 8, p2893-2929, 37p |
| Θεματικοί όροι: | Differential equations, Boundary value problems, Numerical analysis, Artificial neural networks, Fluid mechanics, Extreme learning machines, Orthogonal polynomials, Analytical solutions |
| Περίληψη: | Purpose: This paper aims to provide the approximate solution to variety of differential equations with implicit boundary conditions. Specifically, the focus is on solving higher-order differential equations and system of differential equations, fluid mechanics problem using an orthogonal polynomial-based neural network with extreme learning machine (ELM) algorithm. Design/methodology/approach: The authors use neural network constructed with four different types of orthogonal polynomials: Legendre polynomial, Laguerre polynomial, Chebyshev polynomial and Hermite polynomial and train it using ELM algorithm. The neural network consists of single hidden layer replaced by functional expansion block which uses orthogonal polynomial to extract its features. The result of neural network provides approximate solutions to the problems. To show the capability and efficacy of the approach, obtained solutions are compared with the exact solutions and those derived from traditional numerical technique. Findings: Numerical and comparative studies show that the neural network solutions are obtained with better accuracy. Moreover, the used approach is simple to implement and offer robust framework for solving differential equations with complex boundary conditions. Originality/value: Implicit boundary value problems are successfully addressed, yielding closed form solutions that are highly valuable for real-world applications. Further, the proposed approach for solving implicit problems enhances the applicability of orthogonal polynomial-based neural network with ELM. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://www.emerald.com/insight/content/doi/10.1108/HFF-11-2024-0901 Name: Emerald Insight (All Content) (s7799221) Category: fullText Text: View full text at Emerald MouseOverText: View full text at Emerald |
|---|---|
| Header | DbId: edb DbLabel: Complementary Index An: 188523732 RelevancyScore: 1007 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1007.33666992188 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Orthogonal polynomial-based neural network solution for differential equations with implicit boundary conditions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dey%2C+Shilpa%22">Dey, Shilpa</searchLink><br /><searchLink fieldCode="AR" term="%22Dubey%2C+Shruti%22">Dubey, Shruti</searchLink> – Name: TitleSource Label: Source Group: Src Data: International Journal of Numerical Methods for Heat & Fluid Flow; 2025, Vol. 35 Issue 8, p2893-2929, 37p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+mechanics%22">Fluid mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Extreme+learning+machines%22">Extreme learning machines</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Purpose: This paper aims to provide the approximate solution to variety of differential equations with implicit boundary conditions. Specifically, the focus is on solving higher-order differential equations and system of differential equations, fluid mechanics problem using an orthogonal polynomial-based neural network with extreme learning machine (ELM) algorithm. Design/methodology/approach: The authors use neural network constructed with four different types of orthogonal polynomials: Legendre polynomial, Laguerre polynomial, Chebyshev polynomial and Hermite polynomial and train it using ELM algorithm. The neural network consists of single hidden layer replaced by functional expansion block which uses orthogonal polynomial to extract its features. The result of neural network provides approximate solutions to the problems. To show the capability and efficacy of the approach, obtained solutions are compared with the exact solutions and those derived from traditional numerical technique. Findings: Numerical and comparative studies show that the neural network solutions are obtained with better accuracy. Moreover, the used approach is simple to implement and offer robust framework for solving differential equations with complex boundary conditions. Originality/value: Implicit boundary value problems are successfully addressed, yielding closed form solutions that are highly valuable for real-world applications. Further, the proposed approach for solving implicit problems enhances the applicability of orthogonal polynomial-based neural network with ELM. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edb&AN=188523732 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1108/HFF-11-2024-0901 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 37 StartPage: 2893 Subjects: – SubjectFull: Differential equations Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Fluid mechanics Type: general – SubjectFull: Extreme learning machines Type: general – SubjectFull: Orthogonal polynomials Type: general – SubjectFull: Analytical solutions Type: general Titles: – TitleFull: Orthogonal polynomial-based neural network solution for differential equations with implicit boundary conditions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dey, Shilpa – PersonEntity: Name: NameFull: Dubey, Shruti IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09615539 Numbering: – Type: volume Value: 35 – Type: issue Value: 8 Titles: – TitleFull: International Journal of Numerical Methods for Heat & Fluid Flow Type: main |
| ResultId | 1 |