Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation

Rohollah Bakhshandeh-Chamazkoti and Mohsen Alipour

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 97-107

Abstract: In this paper, the Lie symmetry analysis is proposed for a space–time convection–diffusion fractional differential equations with the Riemann–Liouville derivative by (2+1) independent variables and one dependent variable. We find a reduction form of our governed fractional differential equation using the similarity solution of our Lie symmetry. One-dimensional optimal system of Lie symmetry algebras is found. We present a computational method via the spectral method based on Bernstein’s operational matrices to solve the two-dimensional fractional heat equation with some initial conditions.

Keywords: Bernstein operational matrices; Fractional derivative; Infinitesimal; Lie symmetry; Optimal system; Prolongation; Similarly solution; Spectral method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:97-107

DOI: 10.1016/j.matcom.2022.04.015

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