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arXiv · 2204.08028

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

Rohollah Bakhshandeh-Chamazkoti·Mohsen Alipour
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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.

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Rohollah Bakhshandeh-Chamazkoti, Mohsen Alipour. 2022-04-17. Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation. https://arxiv.org/abs/2204.08028

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