Numerical Solution of Convection-Diffusion Equation by Chebyshev Spectral Method via Lie Group Method

Abstract

The numerical solution of convection-diffusion equation is presented by using Chebyshev spectral method based on El-Gendi method via Lie group analysis. Firstly, we apply Lie symmetry group analysis for the convection-diffusion equation. This method yields convection-diffusion equation to a system of ordinary differential equations (ODEs). Secondly, this system is solved numerically by using Chebyshev spectral method. The numerical results obtained by this way are compared with the exact solution.

Exact solutions of the Harry Dym Equation using Lie group method

“…We apply Lie symmetry group analysis [2,3,7,8,15] for the nonlinear Harry-Dym (HD) equation ( 2) to derive symmetry generators of it. We consider one-parameter  -Lie group point of transformations, which makes equation ( 2 (4) and the third prolongation of the infinitesimal generator ( 4) is given by…”