A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates

Advances in Difference Equations

Mohammed Al-Smadi¹  Andreea Fulga²  Reem Edwan³  Shrideh Al-Omari⁴  Shaher Momani⁵ 

[1] Department of Applied Science, Ajloun College, Al-Balqa Applied University;Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov;Department of Mathematics, Taibah University;Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University;Nonlinear Dynamics Research Center (NDRC), Ajman University;

关键词: Finite volume method;    Finite difference method;    Space fractional convection–diffusion equation;    Riemann–Liouville fractional derivative;    Grünwald–Letnikov fractional derivative;   

DOI  :  10.1186/s13662-021-03669-2

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown