Hello and welcome! My research is on different numerical methods for physical simulations in animation. My focus is on implementing and testing the Parker-Sochacki Method, a relatively new integration technique developed by my professors at James Madison University, and comparing it with numerical methods like Semi-Implicit Euler, Velocity Verlet, and Runge-Kutta 4th Order. Below are videos that compare all 4 methods in terms of flexibility, conservation of energy, and time step size.
The Parker-Sochacki Method converts a system of First Order Initial Value Ordinary Differential Equations into a Maclaurin series up to any order desired. I’ve been researching how Parker-Sochaki performs at lower orders, higher orders, finding more applications, and testing variations on the method. The videos below show that at higher orders, Parker-Sochacki is more flexible in handling a wider range in constants, it conserves energy, and it can take larger time steps than other methods.
VIDEOS THAT COMPARE SEMI-IMPLICIT EULER, VELOCITY VERLET, RUNGE-KUTTA 4TH ORDER, AND PARKER-SOCHACKI
|Flexibility of Springs||Conservation of Energy on a Pendulum||3-Body Largest Possible Time Step|
To see a mathematical step by step for Parker-Sochacki, code, and more animations of a simulation, click on one of the sections above. I also have section for Stereoscopy where I created 3D images of a cornet, Motion Capture where I replicated a form from the James Madison University Tae Kwon Do Club, and a Trumpet Research section where I created a 3D mouthpiece, submerged a trumpet in liquid nitrogen, and experimented with putting helium and Sulfur Hexafluoride through the trumpet.
|Stereoscopy||Motion Capture||Trumpet Tube|