arXiv subjects

Mohsen Alipour

Publications and source records attributed to Mohsen Alipour.

2 recordsLinked to original sources

arXiv2022

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

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.

math.NA↗

arXiv2018

Lie Symmetry Classification and Numerical Analysis of KdV Equation with Power-law Nonlinearity

In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie algebraic classifications and the optimal system are discussed. Finally, using Chebyshev pseudo-spectral method (CPSM), a numerical analysis to solve the invariant solutions corresponded the Lie symmetries of main equation is presented. This method applies the Chebyshev-Gauss-Lobatto points as collocation points.

math.DG↗