An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting
The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouv...
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my.uniten.dspace-365002025-03-03T15:42:44Z An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting Ahmad I. Alshammari A.O. Jan R. Razak N.N.A. Idris S.A. 57220824630 59156924200 57205596279 37059587300 57226267577 The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville?Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources. ? 2024 by the authors. Final 2025-03-03T07:42:44Z 2025-03-03T07:42:44Z 2024 Article 10.3390/fractalfract8060364 2-s2.0-85196879105 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196879105&doi=10.3390%2ffractalfract8060364&partnerID=40&md5=c76915d2defcbb68ea8da526489a419b https://irepository.uniten.edu.my/handle/123456789/36500 8 6 364 All Open Access; Gold Open Access Multidisciplinary Digital Publishing Institute (MDPI) Scopus |
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The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville?Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources. ? 2024 by the authors. |
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57220824630 Ahmad I. Alshammari A.O. Jan R. Razak N.N.A. Idris S.A. |
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Article |
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Ahmad I. Alshammari A.O. Jan R. Razak N.N.A. Idris S.A. |
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Ahmad I. Alshammari A.O. Jan R. Razak N.N.A. Idris S.A. An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| author_sort |
Ahmad I. |
| title |
An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| title_short |
An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| title_full |
An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| title_fullStr |
An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| title_full_unstemmed |
An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo?Lucas?Fibonacci Approach with Strang Splitting |
| title_sort |
efficient numerical solution of a multi-dimensional two-term fractional order pde via a hybrid methodology: the caputo?lucas?fibonacci approach with strang splitting |
| publisher |
Multidisciplinary Digital Publishing Institute (MDPI) |
| publishDate |
2025 |
| _version_ |
1825816184629493760 |
| score |
13.244413 |