A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions
We proposed a Least Squares Finite Element Method (LSFEM) for the approximate solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta-Lucas polynomials expressed in the Caputo fractional sense as basis functions. The LSFEM reduces the TFTE into algebraic system with e...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Scientific African |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227624001157 |
| _version_ | 1797259696452665344 |
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| author | Ebimene James Mamadu Henrietta Ify Ojarikre Simon Ajiroghene Ogumeyo Daniel Chinedu Iweobodo Ebikonbo-Owei Anthony Mamadu Jonathan Tsetimi Ignatius Nkonyeasua Njoseh |
| author_facet | Ebimene James Mamadu Henrietta Ify Ojarikre Simon Ajiroghene Ogumeyo Daniel Chinedu Iweobodo Ebikonbo-Owei Anthony Mamadu Jonathan Tsetimi Ignatius Nkonyeasua Njoseh |
| author_sort | Ebimene James Mamadu |
| collection | DOAJ |
| description | We proposed a Least Squares Finite Element Method (LSFEM) for the approximate solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta-Lucas polynomials expressed in the Caputo fractional sense as basis functions. The LSFEM reduces the TFTE into algebraic system with element matrices and vectors, while the Conjugate Gradient Method (CGM) solved the system for the unknowns with the aid of MAPLE 18. The results generated implies that the proposed method converges favorably to the theoretical solution when the number of elements is large with a large space-time step used for the parameter t. |
| first_indexed | 2024-04-24T23:13:32Z |
| format | Article |
| id | doaj.art-3bb83ed2f72a46c6ae558bcc0e06285c |
| institution | Directory Open Access Journal |
| issn | 2468-2276 |
| language | English |
| last_indexed | 2024-04-24T23:13:32Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj.art-3bb83ed2f72a46c6ae558bcc0e06285c2024-03-17T07:58:34ZengElsevierScientific African2468-22762024-06-0124e02170A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functionsEbimene James Mamadu0Henrietta Ify Ojarikre1Simon Ajiroghene Ogumeyo2Daniel Chinedu Iweobodo3Ebikonbo-Owei Anthony Mamadu4Jonathan Tsetimi5Ignatius Nkonyeasua Njoseh6Department of Mathematics, Delta State University, Abraka, Nigeria; Corresponding author.Department of Mathematics, Delta State University, Abraka, NigeriaDepartment of Mathematics, Delta State University of Science and Technology, Ozoro, Delta State, NigeriaDepartmentof Mathematics, DennisOsadebey University, Asaba, Delta State, NigeriaDepartment of Mathematics, Delta State University, Abraka, NigeriaDepartment of Mathematics, Delta State University, Abraka, NigeriaDepartment of Mathematics, Delta State University, Abraka, NigeriaWe proposed a Least Squares Finite Element Method (LSFEM) for the approximate solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta-Lucas polynomials expressed in the Caputo fractional sense as basis functions. The LSFEM reduces the TFTE into algebraic system with element matrices and vectors, while the Conjugate Gradient Method (CGM) solved the system for the unknowns with the aid of MAPLE 18. The results generated implies that the proposed method converges favorably to the theoretical solution when the number of elements is large with a large space-time step used for the parameter t.http://www.sciencedirect.com/science/article/pii/S2468227624001157Telegraph equationConjugate gradient methodFinite element methodOrthogonal polynomialsVieta-Lucas polynomialsFractional calculus |
| spellingShingle | Ebimene James Mamadu Henrietta Ify Ojarikre Simon Ajiroghene Ogumeyo Daniel Chinedu Iweobodo Ebikonbo-Owei Anthony Mamadu Jonathan Tsetimi Ignatius Nkonyeasua Njoseh A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions Scientific African Telegraph equation Conjugate gradient method Finite element method Orthogonal polynomials Vieta-Lucas polynomials Fractional calculus |
| title | A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions |
| title_full | A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions |
| title_fullStr | A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions |
| title_full_unstemmed | A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions |
| title_short | A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions |
| title_sort | least squares finite element method for time fractional telegraph equation with vieta lucas basis functions |
| topic | Telegraph equation Conjugate gradient method Finite element method Orthogonal polynomials Vieta-Lucas polynomials Fractional calculus |
| url | http://www.sciencedirect.com/science/article/pii/S2468227624001157 |
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