Abstract
The main aim of this thesis is to describe the program Deltasym. It is a Maple program that is designed for interactive use to find Lie point symmetries of ordinary difference equations (ODeltaEs). It is constructed following the method described in Hydon (2000b). Using the linearised symmetry condition of an ODeltaE we can construct a system of determining equations. The solution of system will determine the symmetries of the given ODeltaE. A systematic way to find symmetries of ordinary differential equations (ODEs) given an initial condition is by finding first integrals and reducing the order of the original equation. We investigate this method for finding Lie point symmetries of initial value problems (IVPs) of ODEs and ODeltaEs. This reduction of the IVP may produce more symmetries than the initial problem. Several examples are used to illustrate this surprising fact.