Geometric and algebraic techniques for differential equations

With modelling applications

Symmetry Determination and Linear Differential Equation Package 

Dimsym is a program primarily for the determination of symmetries of differential equations. It also can be used to compute symmetries of distributions of vector fields or differential forms on finite dimensional manifolds, symmetries of geometric objects (e.g. isometries), and also to solve linear partial differential equations.

To use its primary function the user specifies a system of ordinary and/or partial differential equations and the type of symmetry to be found (Lie point, Lie-Backlund or some user-provided ansatz).

Dimsym then produces the corresponding determining equations - a system of linear partial differential equations for the generator of the generic symmetry. It proceeds to solve these equations, reporting any special conditions required to produce a solution. Finally, Dimsym gives the generators of the symmetry group, which may of course be infinite dimensional.

The program allows the user to compute Lie brackets, vector derivatives and so on, and it has an interface with the REDUCE package EXCALC so that all the machinery of calculus on manifolds can be utilised from within the program. Its use can be interactive or batch, and there are extensive tracing options.

If you don't have REDUCE, or if you work on a stand alone IBM compatible, you may wish to use Alan Head's LIE program.

Download Dimsym and related files

Source Code:

Example files:

User's Manual [PDF_270KB] If you require an alternative version of this document, please contact Professor Geoff Prince (G.Prince@latrobe.edu.au)

It is highly recommended that you download the manual and work through the example files. 

Getting Started

Download the Dimsym user's manual.

Given that you want to find symmetries of your differential equation, it is assumed that you know only the basics of REDUCE, such as how to run REDUCE on your machine, and how to compile and load Dimsym, which may vary between different implementations.

More advanced usage of Dimsym such as performing manual manipulations of the determining equations if needed will require greater familiarity with REDUCE, while the user who wants to push the program to its limits may need to be familiar with the algorithms involved.

To learn the basics, chapter 2 of the Dimsym manual features an example to work through. Chapter 17 consists of more examples files to guide you. Read chapter 3 on terminology and chapter 4 on how to best enter your equations and you will be ready to use the program seriously.

Acknowledgement

The development of this program was funded in part by the Australian Research Committee, the Department of Mathematics at La Trobe University, the Department of Mathematics at the University of Wollongong and the CSIRO's Division of Material Science. The author also acknowledges an Australian Postgraduate Research Award.

The authors particularly wish to thank the following beta-testers of the program: Phil Broadbridge, Ted Fackerell, Greg Reid and Willy Sarlet. Special thanks go to Alan Head, the author of LIE, who has been a continuing source of ideas and assistance. We also thank Charles Wright for his assistance in integrating his REDUCE ODESOLVE package into Dimsym.

Authors

James Sherring, Geoff Prince and Michael Jerie