alexa Lie Group Analysis for Solving the Problem of Diffusion
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Abd-el-Malek MB1,2* and Amin AM1

1Department of Engineering Mathematics and Physics, Alexandria University, Alexandria 21544, Egypt

2Department of Mathematics and Actuarial Science, The American University in Cairo, New Cairo 11835, Egypt

Corresponding Author:
Abd-el-Malek MB
Department of Engineering Mathematics and Physics
Faculty of Engineering, Alexandria University
Alexandria 21544, Egypt,
Tel: 01000066496
E-mail: [email protected]

Received date: August 10, 2015; Accepted date: November 20, 2015; Published date: November 25, 2015

Citation: Abd-el-Malek MB, Amin AM (2015) Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane. J Generalized Lie Theory Appl 9:236. doi:10.4172/1736-4337.1000236

Copyright: © 2015 Abd-el-Malek MB, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

The Lie group method is applied to study the diffusion process of drugs across a biological membrane which tends to partially absorb the drug. For the diffusion coefficient, we considered two cases. The Lie group analysis is based on reducing the number of independent variables by one, and consequently the mathematical model described by nonlinear partial differential equation to, covers the diffusion process with the boundary and initial conditions, and is transformed into an ordinary differential equation with the corresponding conditions. The obtained nonlinear ordinary differential equation is solved numerically using the 4th and 5th Runge Kutta method, and the results are illustrated graphically and in tables too.

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