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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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124001657 |
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| author | Shams Ul Arifeen Ihteram Ali Imtiaz Ahmad Sadaf Shaheen |
| author_facet | Shams Ul Arifeen Ihteram Ali Imtiaz Ahmad Sadaf Shaheen |
| author_sort | Shams Ul Arifeen |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a0db500b8a5e4091b73b4a2cec4fa302 |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-a0db500b8a5e4091b73b4a2cec4fa3022025-08-20T02:50:13ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210077910.1016/j.padiff.2024.100779Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin’s methodShams Ul Arifeen0Ihteram Ali1Imtiaz Ahmad2Sadaf Shaheen3Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Peshawar, 25000, KP, Pakistan; Corresponding author.Department of Mathematics and Statistics, Women University Swabi, Swabi 23430, PakistanInstitute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, MalaysiaDepartment of Mathematics, University of Mianwali, Mianwali, PakistanThis 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.http://www.sciencedirect.com/science/article/pii/S2666818124001657B-splineGauss quadratureGalerkin methodKawahara equations |
| spellingShingle | Shams Ul Arifeen Ihteram Ali Imtiaz Ahmad Sadaf Shaheen Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin’s method Partial Differential Equations in Applied Mathematics B-spline Gauss quadrature Galerkin method Kawahara equations |
| 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 |
| topic | B-spline Gauss quadrature Galerkin method Kawahara equations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124001657 |
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