Perturbed ODEs in Cosmology and Invariance Analysis of Ordinary Difference Equations

• Main Author: Mnguni, Nkosingiphile
• Format: Others
• Language: en
• Published: 2018
• Online Access: https://hdl.handle.net/10539/25019

A dissertation submitted to the faculty of science, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science, Johannesburg December 2017 === This dissertation contains two parts ,the first part involves the novel study of the use of symmetries to find exact solutions of ordinary difference equations. Non-trivial symmetries of third-order difference equations of the form (1) are obtained. These symmetries are used to investigate their solutions for some random sequences (An) and (Bn). We extend the results obtained in [15] and conditions for well-defined solutions are obtained. Furthermore, a full Lie point symmetry analysis of the fifthorder rational difference equations of the form (5), where λ and µ are real numbers, is considered and exact solutions are found. In the second part we find new geometric conditions that can be specialized to obtain the approximate Noether symmetries of a large class of variational equations. We will also look at the ordinary differential equations that model cosmological and relativistic phenomena, which we will analyse using an approximate symmetry method. === XL2018