A FINITE DIFFERENCE METHOD ON UNIFORM MESHES FOR SOLVING THE TIME-SPACE FRACTIONAL ADVECTION-DIFFUSION EQUATION

Allaoua Boudjedour; Iqbal M. Batiha; Selma Boucetta; Mohamed Dalah; Khaled Zennir; Adel Ouannas

doi:10.56947/gjom.v19i1.2524

A FINITE DIFFERENCE METHOD ON UNIFORM MESHES FOR SOLVING THE TIME-SPACE FRACTIONAL ADVECTION-DIFFUSION EQUATION

Allaoua Boudjedour
, Iqbal M. Batiha
, Selma Boucetta
, Mohamed Dalah
, Khaled Zennir
, Adel Ouannas

Nonlinear Dynamic Research Centre (NDRC)

Frères Mentouri Constantine 1 University
Al-Zaytoonah University of Jordan
Qassim University
University of Oum El Bouaghi

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

In order to investigate linear time and spatial fractional advection equations, we present a finite difference scheme (FDS) in this paper. The fractional Taylor series method for u at t_j+1 and x_i+1 is used to approximate the fractional derivatives. First, we construct our numerical scheme (NS) for the mathematical model. In the second part, we study the stability and convergence of our numerical scheme. Finally, the numerical simulations of the fractional advection equation, using the FDM, is plotted for several values of fractional parameters α and ν. It will be shown that the convergence is achieved properly which confirms the effectiveness of the proposed algorithm.

Original language	English
Pages (from-to)	156-168
Number of pages	13
Journal	Gulf Journal of Mathematics
Volume	19
Issue number	1
DOIs	https://doi.org/10.56947/gjom.v19i1.2524
State	Published - 2025

Keywords

Fractional derivatives
consistence
convergence
finite difference scheme
fractional Taylor series method
fractional advection equation
stability

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10.56947/gjom.v19i1.2524

Cite this

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title = "A FINITE DIFFERENCE METHOD ON UNIFORM MESHES FOR SOLVING THE TIME-SPACE FRACTIONAL ADVECTION-DIFFUSION EQUATION",

abstract = "In order to investigate linear time and spatial fractional advection equations, we present a finite difference scheme (FDS) in this paper. The fractional Taylor series method for u at tj+1 and xi+1 is used to approximate the fractional derivatives. First, we construct our numerical scheme (NS) for the mathematical model. In the second part, we study the stability and convergence of our numerical scheme. Finally, the numerical simulations of the fractional advection equation, using the FDM, is plotted for several values of fractional parameters α and ν. It will be shown that the convergence is achieved properly which confirms the effectiveness of the proposed algorithm.",

keywords = "Fractional derivatives, consistence, convergence, finite difference scheme, fractional Taylor series method, fractional advection equation, stability",

author = "Allaoua Boudjedour and Batiha, \{Iqbal M.\} and Selma Boucetta and Mohamed Dalah and Khaled Zennir and Adel Ouannas",

year = "2025",

doi = "10.56947/gjom.v19i1.2524",

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T1 - A FINITE DIFFERENCE METHOD ON UNIFORM MESHES FOR SOLVING THE TIME-SPACE FRACTIONAL ADVECTION-DIFFUSION EQUATION

AU - Boudjedour, Allaoua

AU - Batiha, Iqbal M.

AU - Boucetta, Selma

AU - Dalah, Mohamed

AU - Zennir, Khaled

AU - Ouannas, Adel

PY - 2025

Y1 - 2025

N2 - In order to investigate linear time and spatial fractional advection equations, we present a finite difference scheme (FDS) in this paper. The fractional Taylor series method for u at tj+1 and xi+1 is used to approximate the fractional derivatives. First, we construct our numerical scheme (NS) for the mathematical model. In the second part, we study the stability and convergence of our numerical scheme. Finally, the numerical simulations of the fractional advection equation, using the FDM, is plotted for several values of fractional parameters α and ν. It will be shown that the convergence is achieved properly which confirms the effectiveness of the proposed algorithm.

AB - In order to investigate linear time and spatial fractional advection equations, we present a finite difference scheme (FDS) in this paper. The fractional Taylor series method for u at tj+1 and xi+1 is used to approximate the fractional derivatives. First, we construct our numerical scheme (NS) for the mathematical model. In the second part, we study the stability and convergence of our numerical scheme. Finally, the numerical simulations of the fractional advection equation, using the FDM, is plotted for several values of fractional parameters α and ν. It will be shown that the convergence is achieved properly which confirms the effectiveness of the proposed algorithm.

KW - Fractional derivatives

KW - consistence

KW - convergence

KW - finite difference scheme

KW - fractional Taylor series method

KW - fractional advection equation

KW - stability

UR - https://www.scopus.com/pages/publications/85216493013

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DO - 10.56947/gjom.v19i1.2524

M3 - Article

AN - SCOPUS:85216493013

SN - 2309-4966

VL - 19

SP - 156

EP - 168

JO - Gulf Journal of Mathematics

JF - Gulf Journal of Mathematics

IS - 1

ER -

A FINITE DIFFERENCE METHOD ON UNIFORM MESHES FOR SOLVING THE TIME-SPACE FRACTIONAL ADVECTION-DIFFUSION EQUATION

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Keywords

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