The program that I worked with for this project uses the relativistic Hartree-Fock approximation to calculate the equation of state of dense neutron star matter. The code was originally developed in Dr. Weber’s group, but had some serious issues requiring rewriting. I was initially unable to compile the code due to corruption issues and changes in the version of the NAG (Numerical Algorithm Group) library being used. Fixing these problems was the first part of the project, after which I was able to use the code to perform further studies. In this thesis I will present results from repeating a series of calculations of dense neutron star matter characteristics for symmetric nuclear matter. I will then present the results of implementing three different optimization subroutines that I wrote to increase the domain of convergence of the original code. Calculations of the speed of sound in the medium for a combination of very high particle density and an inflated ω-meson coupling constant will then be presented. I chose to increase the ω-meson coupling constant because it is responsible for inter-baryon repulsion and increasing it should reveal issues with the approximation, if there are any. The results of these speed of sound calculations show that the code obeys causality (cs < c), as it should being an implementation of a relativistic theory, even at the (unphysical) intersection of extremely high density and an inflated ω-meson coupling constant. In the future it would be worth testing these results in versions of the model where the meson coupling constant varies, depending on the conditions, throughout the simulation. We also plan to extend these methods to versions of the code that calculate the nuclear equation of state for matter in chemical equilibrium and at finite temperatures, as encountered in the dense cores of neutron stars.