The Determination of Nonlocal Symmetries by the Technique of Reduction of Order

Autonomous systems of ordinary differential equations can be rewritten as systems of first order ordinary differential equations and one of the dependent variables chosen as a new independent variable. Some of the variables are eliminated to give a mixed system of first and second order equations for which the determination of point symmetries can be automated without having to make an Ansatz on the detailed structure of the symmetry. Because the coefficient function for the original independent variable appears only as its derivative in the reduced system, symmetries which are nonlocal in this variable become local symmetries of the reduced system and can be computed algorithmically