Numerical Approximation of a Nonlinear Fractional Elliptic System

Authors

Sara Dob, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), Department of Mathematics, Faculty of Science, University 20 august 1955, Skikda, AlgeriaFollow
Messaoud Maouni, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), Department of Mathematics, Faculty of Science, University 20 august 1955, Skikda, AlgeriaFollow
Kamel Slimani, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), Department of Mathematics, Faculty of Science, University 20 august 1955, Skikda, AlgeriaFollow
Hakim Lakhal, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), Department of Mathematics, Faculty of Science, University 20 august 1955, Skikda, AlgeriaFollow

Author Country (or Countries)

Algeria

Abstract

This paper proposes a fractional numerical approximation of elliptic system with fractional order (s ∈]0, 1[) via the finite difference method (FDM), the analysis is performed on two general dimensional domains with homogeneous boundary conditions. A convergent series solution and the corresponding error estimates are obtained. The performance of FDM is tested with known exact solution, which confirm the theoretical predictions.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160109

Recommended Citation

Dob, Sara; Maouni, Messaoud; Slimani, Kamel; and Lakhal, Hakim (2022) "Numerical Approximation of a Nonlinear Fractional Elliptic System," Applied Mathematics & Information Sciences: Vol. 16: Iss. 1, Article 9.
DOI: http://dx.doi.org/10.18576/amis/160109
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss1/9