Introduction to Symmetry Analysis, Exercises of Differential Equations

Download Introduction to Symmetry Analysis and more Exercises Differential Equations in PDF only on Docsity!

Introduction to Symmetry Analysis

Brian Cantwell

Department of Aeronautics and Astronautics

Stanford University

Chapter 9 - Partial Differential Equations

Finite transformation of partial derivatives

Variable count

Infinitesimal transformation of the first partial derivative

The (p-1)th order extended infinitesimal transformation is

The number of terms in the infinitesimal versus the derivative order

Isolating the determining equations of the group - the Lie algorithm

The classical point group of the heat equation

The fully expanded invariance condition is

Apply the constraint that the solution must satisfy the

heat equation and gather terms

The determining equations of the point group of the heat equation

The classical six parameter group of the heat equation

Use the software to work out the groups of the heat equation in 3D