Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

Computation and Pre-Parametric Design

My work is broadly concerned with the question "How can designs bessynthesized computationally?" The project deals primarily with mechanical devices and focuses on pre-parametric design: design at the level of detail of a blackboard sketch rather than at the level of detail of an engineering drawing. I explore the project ideas in the domain of single-input single-output dynamic systems, like pressure gauges, accelerometers, and pneumatic cylinders. The problem solution consists of two steps: 1) generate a schematic description of the device in terms of idealized functional elements, and then 2) from the schematic description generate a physical description.