### Numerical analysis of difference equations from loop quantum cosmology

A collaboration with Physics department faculty. Numerical solution of difference equations that arise as a result of quantum theory applied to models of cosmology and black holes. The stability and convergence of difference equations were analyzed using von Neumann analysis. High order approximation methods are applied to the difference equation systems to properly deal with the instabilities which occur noticeably over time. The evolution of the wave function is investigated through this analysis.