Barycentric Legendre interpolation method for solving nonlinear fractal-fractional Burgers equation

Authors

  • Arezou Rezazadeh Department of Mathematics, University of Qom, Qom 37161466711, Iran
  • Abdelhameed M. Nagy Department of Mathematics, Faculty of Science, Kuwait University, Safat 13060, Kuwait
  • Zakieh Avazzadeh Department of Applied Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China

DOI:

https://doi.org/10.30495/jme.v15i0.2009

Keywords:

Burgers equation, Fractal-fractional derivative, Barycenteric interpolation method, Legendre polynomials, Operational matrix

Abstract

In this paper, we formulate a numerical method to approximate  the  solution of non-linear fractal-fractional Burgers equation. In this model, differential operators are defined in the Atangana-Riemann-Liouville sense with Mittage-Leffler kernel. We first expand the spatial derivatives using barycentric interpolation method and then we derive an operational matrix (OM) of the fractal-fractional derivative for the Legendre polynomials. To be more precise, two approximation tools are coupled to convert the fractal-fractional Burgers equation into a  system of  algebraic equations which is technically uncomplicated and can be solved using available mathematical software such as MATLAB.  To investigate the agreement between exact  and approximate solutions, several examples are examined.

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Published

2021-08-06

Issue

Vol. 15

Section

Vol. 15, No. 5, (2021)

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