Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation
A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion model is considered in this paper. Based on finite difference schemes, we formulate both second-order and fourth-order numerical methods for the approximation of the Riesz space fractional reaction–diffusion-like e...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000773 |
| _version_ | 1797390343456423936 |
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| author | Kolade M. Owolabi |
| author_facet | Kolade M. Owolabi |
| author_sort | Kolade M. Owolabi |
| collection | DOAJ |
| description | A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion model is considered in this paper. Based on finite difference schemes, we formulate both second-order and fourth-order numerical methods for the approximation of the Riesz space fractional reaction–diffusion-like equation of Fisher type. In the experiment, it was observed that the fourth-order scheme has better accuracy than the second-order method when applied to solve the fractional diffusion equation. It should be mentioned that the lower order scheme computes rapidly and save more computational time as displayed in the table of results. Finally, some simulation results are presented to justify the effectiveness and applicability of the numerical methods. The one- two- and three-dimensional results obtained for some instances of fractional order (α,β) depict some amazing complex and spatiotemporal patterns which are applicable in applied sciences and engineering. |
| first_indexed | 2024-03-08T23:10:20Z |
| format | Article |
| id | doaj.art-5aefcf74efa84433a851a2f0f0d5d711 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:20Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-5aefcf74efa84433a851a2f0f0d5d7112023-12-15T07:26:48ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100564Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equationKolade M. Owolabi0Department of Mathematical Sciences, Federal University of Technology Akure, PMB 704, Akure, Ondo State, NigeriaA Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion model is considered in this paper. Based on finite difference schemes, we formulate both second-order and fourth-order numerical methods for the approximation of the Riesz space fractional reaction–diffusion-like equation of Fisher type. In the experiment, it was observed that the fourth-order scheme has better accuracy than the second-order method when applied to solve the fractional diffusion equation. It should be mentioned that the lower order scheme computes rapidly and save more computational time as displayed in the table of results. Finally, some simulation results are presented to justify the effectiveness and applicability of the numerical methods. The one- two- and three-dimensional results obtained for some instances of fractional order (α,β) depict some amazing complex and spatiotemporal patterns which are applicable in applied sciences and engineering.http://www.sciencedirect.com/science/article/pii/S2666818123000773Caputo-time derivativeRiesz-space derivativeFourier spectral methodFractional reaction–diffusion equationNumerical simulations |
| spellingShingle | Kolade M. Owolabi Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation Partial Differential Equations in Applied Mathematics Caputo-time derivative Riesz-space derivative Fourier spectral method Fractional reaction–diffusion equation Numerical simulations |
| title | Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation |
| title_full | Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation |
| title_fullStr | Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation |
| title_full_unstemmed | Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation |
| title_short | Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation |
| title_sort | computational study for the caputo sub diffusive and riesz super diffusive processes with a fractional order reaction diffusion equation |
| topic | Caputo-time derivative Riesz-space derivative Fourier spectral method Fractional reaction–diffusion equation Numerical simulations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000773 |
| work_keys_str_mv | AT kolademowolabi computationalstudyforthecaputosubdiffusiveandrieszsuperdiffusiveprocesseswithafractionalorderreactiondiffusionequation |