Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations

Abstract

We apply the method of preliminary group classification to ordinary differential equations of the formy(n)=E(x,y,y',…,y(n-1),fi(x)),  i=0,…,m.We show how this method can be implemented via the popular symmetry analysis packagePROGRAM LIEprovided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given byy′′=∑i=25fixyi.