A fundamental problem in astrophysics involves the origin of jets and the dynamics of accretion disks. How does a collimated outflow arise from hot material that is spiraling into a central object (be it a black hole, neutron star, white dwarf or young star)? Why do jets appear to turn "on" and "off" as the accretion disk changes between different states?

In this thesis, we attempt to shed some light on this question through observational, theoretical and computational studies. We present high time resolution observations of the Galactic black hole candidate GRS 1915+105 and show how subtle differences in the accretion disk evolution in this object during different episodes of activity are related to different types of jet ejections. We then develop several new theoretical results about accretion disks that allow us to parametrize our uncertainty about the jet and other complex physics in a way that can be studied in one- or two-dimensional numerical simulations. Following this, we present FRIENDLY, a new code for numerical integration of arbitrary partial differential equations to arbitrary orders of accuracy that was developed during the course of this thesis. Finally, we present a preliminary application of FRIENDLY, in which we attempt to simulate an accretion disk that experiences a sudden increase in the strength of turbulence, as might be expected if an ordered magnetic field were ejected from the system in the form of a jet. We compare the simulations to the observations of GRS 1915+105 and conclude that further study of this mechanism may lead to an explanation for the behavior of this enigmatic object.