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

Authors
  • Edwan, Reem1
  • Al-Omari, Shrideh2
  • Al-Smadi, Mohammed3, 4
  • Momani, Shaher4, 5
  • Fulga, Andreea6
  • 1 Taibah University, Al Madinah Al Munawara, Saudi Arabia , Al Madinah Al Munawara (Saudi Arabia)
  • 2 Al-Balqa Applied University, Amman, Jordan , Amman (Jordan)
  • 3 Al-Balqa Applied University, Ajloun, 26816, Jordan , Ajloun (Jordan)
  • 4 Ajman University, Ajman, UAE , Ajman (United Arab Emirates)
  • 5 University of Jordan, Amman, 11942, Jordan , Amman (Jordan)
  • 6 Universitatea Transilvania Brasov, Brasov, Romania , Brasov (Romania)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Nov 29, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03669-2
Source
Springer Nature
Keywords
Disciplines
  • Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential E
License
Green

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.

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