A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term
In this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682401158X |
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| author | Allaoua Mehri Hakima Bouhadjera Mohammed S. Abdo Najla Alghamdi Sahar Ahmed Idris |
| author_facet | Allaoua Mehri Hakima Bouhadjera Mohammed S. Abdo Najla Alghamdi Sahar Ahmed Idris |
| author_sort | Allaoua Mehri |
| collection | DOAJ |
| description | In this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the convergence is of order 2-α in time, and 2-β in space, for 0<α;β<1. Results of conditional stability and convergence of the numerical method are discussed. Finally a numerical implementation was presented to show the conformity between the theoretical and numerical approach of the finite difference scheme. |
| format | Article |
| id | doaj-art-1f02cec2c44641b3b975627f4e3f675c |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-1f02cec2c44641b3b975627f4e3f675c2025-01-09T06:13:21ZengElsevierAlexandria Engineering Journal1110-01682025-01-01110186192A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order termAllaoua Mehri0Hakima Bouhadjera1Mohammed S. Abdo2Najla Alghamdi3Sahar Ahmed Idris4Department of Mathematics, University of Chadli Ben Djedid, El-Tarf, AlgeriaDepartment of Mathematics, Badji Mokhtar-Annaba University, Annaba, AlgeriaDepartment of Mathematics, Hodeidah University, Al-Hudaydah, 3114, Yemen; Corresponding author.Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Industrial Engineering, Faculty of Engineering, King Khalid University, Abha, Saudi ArabiaIn this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the convergence is of order 2-α in time, and 2-β in space, for 0<α;β<1. Results of conditional stability and convergence of the numerical method are discussed. Finally a numerical implementation was presented to show the conformity between the theoretical and numerical approach of the finite difference scheme.http://www.sciencedirect.com/science/article/pii/S111001682401158XTransport equation of fractional orderNumerical schemeStabilityConvergence |
| spellingShingle | Allaoua Mehri Hakima Bouhadjera Mohammed S. Abdo Najla Alghamdi Sahar Ahmed Idris A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term Alexandria Engineering Journal Transport equation of fractional order Numerical scheme Stability Convergence |
| title | A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term |
| title_full | A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term |
| title_fullStr | A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term |
| title_full_unstemmed | A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term |
| title_short | A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term |
| title_sort | new error estimate of a finite difference scheme for a fractional transport advection equation with zero order term |
| topic | Transport equation of fractional order Numerical scheme Stability Convergence |
| url | http://www.sciencedirect.com/science/article/pii/S111001682401158X |
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