Resonant tunneling diodes (RTDs) are ultra-small semiconductor devices that have potential as very high frequency oscillators. To describe the electron transport within these devices, the Wigner-Poisson Equations are used. These equations incorporate quantum mechanics to describe how the electron distribution changes in time due to kinetic energy, potential energy, and scattering effects. To study the RTD, we apply numerical continuation methods to calculate the steady-state electron distribution as the voltage difference across the RTD varies. To implement the continuation methods, the RTD simulator is interfaced to LOCA (Library of Continuation Algorithm), a software library that is a part of Sandia National Laboratories' parallel solver package, Trilinos. With more sophisticated numerical solvers, we are able to calculate solutions on finer grids that were previously too computationally intensive. This is very important to allow for detailed studies of correlation effects which may dramatically influence oscillatory behavior in RTD-based devices. The more accurate results derived from this work reveal new physical effects that were absent in prior studies. Hence, these physics-based and more refined numerical simulations will provide new insights and greatly facilitate the future optimization of RTD-based oscillator sources and thus has important relevance to THz-frequency-regime based spectroscopic sensing technology.