Lie Symmetry Method for Solutions of Differential Equations with Applications in Physics

Year 2015, Volume: 36 Issue: 3, 2223 - 2233, 13.05.2015

Seyed Reza Hejazı , Elaheh Saberı Paeezeh Mahdavı

Abstract

Abstract. A mathematical method in pure mathematics (differential geometry) for finding solutions of differential equations is considered. The method is based on constructing a Lie algebra associated to a given system of differential equation, called Lie algebra of the symmetries of the given system. This Lie algebra is a vector space which maps a given solution, such as a constant solution, to another solution, it is a significant tool for finding new solution for system of differential equation specially partial differential equations. Then we will apply it to some differential equations in fluid mechanics and physics.

Keywords

Differential equations, Fluid Mechanics, boundary layers, Newtonian fluid, Flows of vector fields, heat transfer equation

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