Physical Sciences and Mathematics Commons^™

Application Of The Fokker-Planck Equation For Quantifying Initial Condition Uncertainty Of Reversible Dynamic Systems, Troy S. Newhart

Mechanical & Aerospace Engineering Theses & Dissertations

Characterizing the behavior of dynamic systems requires the inclusion of initial conditions to propagate behavior forward in time. More realistic representations of system behavior quantify uncertainty about the initial conditions to assess sensitivity, reliability, and other stochastic response parameters. In many engineering applications, the uncertain initial conditions may be unknown given a desired response. This research applies the Fokker-Planck equation to reversible dynamic systems of select multi-dimensional nonlinear differential equations as a means for predicting the uncertainty about initial conditions. An alternating directions implicit numerical scheme is used to numerically solve the Fokker-Planck equation for both forward and reversed equations …