Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method
This study presents two numerical methods focused on Quintic B-spline (QBS) and Galerkin finite element method (GFEM) for solving time-fractional Kawahara equations. The QBS is utilized as both the basis and test function in the FEM approach. We apply Caputo formula with quadrature rule for evaluati...
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Elsevier B.V.
2025
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| author | Arifeen S.U. Ali I. Ahmad I. Shaheen S. |
| author2 | 57204288243 |
| author_facet | 57204288243 Arifeen S.U. Ali I. Ahmad I. Shaheen S. |
| author_sort | Arifeen S.U. |
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| content_provider | Universiti Tenaga Nasional |
| content_source | UNITEN Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | This study presents two numerical methods focused on Quintic B-spline (QBS) and Galerkin finite element method (GFEM) for solving time-fractional Kawahara equations. The QBS is utilized as both the basis and test function in the FEM approach. We apply Caputo formula with quadrature rule for evaluation of temporal fractional part. The QBS and GFEM formulation are used to approximate the space functions and their derivatives. Furthermore, a four-point Gauss Legendre quadrature is employed to evaluate the source term in the GFEM. The efficiency and accuracy of the proposed scheme are evaluated using the E2 and E� norms. Additionally, Fourier stability analysis is conducted, and it is revealed that the method exhibits unconditional stability. The results, presented in the form of tables and graphs to demonstrate the effectiveness of the scheme. ? 2024 The Author(s) |
| format | Article |
| id | my.uniten.dspace-36117 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2025 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | my.uniten.dspace-361172025-03-03T15:41:24Z Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method Arifeen S.U. Ali I. Ahmad I. Shaheen S. 57204288243 57211855967 57220824630 57697237900 This study presents two numerical methods focused on Quintic B-spline (QBS) and Galerkin finite element method (GFEM) for solving time-fractional Kawahara equations. The QBS is utilized as both the basis and test function in the FEM approach. We apply Caputo formula with quadrature rule for evaluation of temporal fractional part. The QBS and GFEM formulation are used to approximate the space functions and their derivatives. Furthermore, a four-point Gauss Legendre quadrature is employed to evaluate the source term in the GFEM. The efficiency and accuracy of the proposed scheme are evaluated using the E2 and E� norms. Additionally, Fourier stability analysis is conducted, and it is revealed that the method exhibits unconditional stability. The results, presented in the form of tables and graphs to demonstrate the effectiveness of the scheme. ? 2024 The Author(s) Final 2025-03-03T07:41:24Z 2025-03-03T07:41:24Z 2024 Article 10.1016/j.padiff.2024.100779 2-s2.0-85208270715 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85208270715&doi=10.1016%2fj.padiff.2024.100779&partnerID=40&md5=47fb261917ee62532529c593eeaa5030 https://irepository.uniten.edu.my/handle/123456789/36117 12 100779 All Open Access; Gold Open Access Elsevier B.V. Scopus |
| spellingShingle | Arifeen S.U. Ali I. Ahmad I. Shaheen S. Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title | Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title_full | Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title_fullStr | Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title_full_unstemmed | Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title_short | Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin's method |
| title_sort | computational study of time-fractional non-linear kawahara equations using quintic b-spline and galerkin's method |
| url_provider | http://dspace.uniten.edu.my/ |