The exact solutions of some rational difference equations with Lie symmetry analysis

This thesis involves the study of symmetries to find the exact solutions of some rational difference equations. We obtain the solutions for special cases of the difference equations by using Lie symmetry analysis. This thesis consist of six chapter. In the first chapter, we introduce the difference equations and Lie symmetry analysis. Also we give a brief literature review of studies about the thesis topic. In the second chapter, we give some basic definitions and theorems needed in this thesis. In the third chapter, we consider an example of difference equation which the exact solutions obtained by Lie symmetry analysis. In the fourth chapter, we investigate the Lie point symmetries of some fifth order difference equations and obtain their exact solutions with Lie symmetry analysis. In the fifth chapter, we give the exact solutions of some higher order rational difference equation by using Lie symmetry analysis. In the final chapter, apart from the form of the difference equations which is mentioned in the other chapters, we consider a different type of difference equation and obtain the exact solutions.