A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method
In this manuscript, the collocation approach using the higher order extended cubic B-spline (ECBS) as the basis function is efficiently used to numerically solve the generalized time fractional Burger-Huxley equation (TFBHE). The Burger-Huxley equation is a widely studied nonlinear partial different...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-11-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723009129 |
| _version_ | 1797615909244764160 |
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| author | Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong |
| author_facet | Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong |
| author_sort | Tayyaba Akram |
| collection | DOAJ |
| description | In this manuscript, the collocation approach using the higher order extended cubic B-spline (ECBS) as the basis function is efficiently used to numerically solve the generalized time fractional Burger-Huxley equation (TFBHE). The Burger-Huxley equation is a widely studied nonlinear partial differential equation that models the propagation of nerve impulses in excitable systems such as the neurons in the brain. The time fractional versions of the Burger-Huxley equation (BHE), which incorporate fractional derivatives in time direction to model the anomalous diffusion, reaction mechanism, and memory effects observed in many physical and biological systems. The θ−weighted technique and the Atangana–Baleanu operator are employed to discretize the equation. The higher order EBCS method is used in space direction. The stability and convergence analysis are also presented. Numerous examples are carried out to show the validity of the technique. The graphical representations and computed results are observed the good agreement with the literature. |
| first_indexed | 2024-03-11T07:33:40Z |
| format | Article |
| id | doaj.art-2fffc1ea0e5a422ab1787cf5cfb5bd8b |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:33:40Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
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| series | Results in Physics |
| spelling | doaj.art-2fffc1ea0e5a422ab1787cf5cfb5bd8b2023-11-17T05:26:36ZengElsevierResults in Physics2211-37972023-11-0154107119A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order methodTayyaba Akram0Azhar Iqbal1Poom Kumam2Thana Sutthibutpong3Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road Bang Mod, Thung Khru, Bangkok 10140, ThailandMathematics and Natural Sciences, Prince Mohammad Bin Fahd University, 31952 Al Khobar, Kingdom of Saudi ArabiaCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road Bang Mod, Thung Khru, Bangkok 10140, Thailand; Theoretical and Computational Physics Group, Department of Physics, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road Bang Mod, Thung Khru, Bangkok 10140, Thailand; Theoretical and Computational Physics Group, Department of Physics, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand; Corresponding author.In this manuscript, the collocation approach using the higher order extended cubic B-spline (ECBS) as the basis function is efficiently used to numerically solve the generalized time fractional Burger-Huxley equation (TFBHE). The Burger-Huxley equation is a widely studied nonlinear partial differential equation that models the propagation of nerve impulses in excitable systems such as the neurons in the brain. The time fractional versions of the Burger-Huxley equation (BHE), which incorporate fractional derivatives in time direction to model the anomalous diffusion, reaction mechanism, and memory effects observed in many physical and biological systems. The θ−weighted technique and the Atangana–Baleanu operator are employed to discretize the equation. The higher order EBCS method is used in space direction. The stability and convergence analysis are also presented. Numerous examples are carried out to show the validity of the technique. The graphical representations and computed results are observed the good agreement with the literature.http://www.sciencedirect.com/science/article/pii/S2211379723009129Time fractional reaction–diffusion modelB-spline basisAtangana–Baleanu derivative |
| spellingShingle | Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method Results in Physics Time fractional reaction–diffusion model B-spline basis Atangana–Baleanu derivative |
| title | A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method |
| title_full | A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method |
| title_fullStr | A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method |
| title_full_unstemmed | A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method |
| title_short | A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method |
| title_sort | newly constructed numerical approximation and analysis of generalized fractional burger huxley equation using higher order method |
| topic | Time fractional reaction–diffusion model B-spline basis Atangana–Baleanu derivative |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723009129 |
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