Comparitive Study Of A In Homogeneous Nonlinear Diffusion Equation By Similarity Method And Its Exactedness

Research Article
Sivakami L
DOI: 
http://dx.doi.org/10.24327/ijrsr.2017.0807.0561
Subject: 
science
KeyWords: 
Diffusion Equation- Lie Point symmetric vector field.
Abstract: 

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, it is important to seek their exact solutions. The classical Lie symmetry method can be used to find similarity solutions systematically. The motivation for the present study is to carry over these techniques, either singly or collectively for obtaining the nonlinear diffusion equation and its symmetry reductions, namely, the second-order nonlinear ordinary differential equations via the isovector approach. The fundamental basis of the techniques is that, when a differential equation is invariant under a Lie group transformations, a reduction transformation exists. The machinery of the Lie group theory provides a systematic method to search for these special group invariant solutions. In this work, I introduce and proved a reduction theorem that will help us to make some critical reduction answer without having to do any teadious calculation