A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates
Abstract Convection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this contex...
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2021
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oai:doaj.org-article:b6dec11c6c1f4bb0a927d1f21c16b94e2021-12-05T12:07:09ZA new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates10.1186/s13662-021-03669-21687-1847https://doaj.org/article/b6dec11c6c1f4bb0a927d1f21c16b94e2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03669-2https://doaj.org/toc/1687-1847Abstract Convection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method.Reem EdwanShrideh Al-OmariMohammed Al-SmadiShaher MomaniAndreea FulgaSpringerOpenarticleFinite volume methodFinite difference methodSpace fractional convection–diffusion equationRiemann–Liouville fractional derivativeGrünwald–Letnikov fractional derivativeMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-19 (2021) |
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DOAJ |
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DOAJ |
| language |
EN |
| topic |
Finite volume method Finite difference method Space fractional convection–diffusion equation Riemann–Liouville fractional derivative Grünwald–Letnikov fractional derivative Mathematics QA1-939 |
| spellingShingle |
Finite volume method Finite difference method Space fractional convection–diffusion equation Riemann–Liouville fractional derivative Grünwald–Letnikov fractional derivative Mathematics QA1-939 Reem Edwan Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani Andreea Fulga A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| description |
Abstract Convection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method. |
| format |
article |
| author |
Reem Edwan Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani Andreea Fulga |
| author_facet |
Reem Edwan Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani Andreea Fulga |
| author_sort |
Reem Edwan |
| title |
A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| title_short |
A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| title_full |
A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| title_fullStr |
A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| title_full_unstemmed |
A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| title_sort |
new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/b6dec11c6c1f4bb0a927d1f21c16b94e |
| work_keys_str_mv |
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