Hello and welcome to my research page. My focus is on applying the Parker-Sochacki Method to different physical simulations comparing it against numerical methods currently used in the animation industry.
There is also a section for Motion Capture, Stereoscopy, and Trumpet Research.
N-Body Gravity: Comparing Different Integrators
Here you will see images of a 3-body gravity problem all under the same initial conditions following this pattern:
I am going to show that at higher orders, Parker-Sochacki can take the largest time step maintaining accuracy compared to Forward Euler, Semi-Implicit Euler, Velocity Verlet, Runge-Kutta 2 Midpoint Method, and Runge-Kutta 4th Order. At 8th Order, Parker-Sochacki can take a time step of 0.001 for this 3 body problem. I will show what the other integrators look like at that same time step followed by what time step they need to have the same accuracy as Parker-Sochacki.
Forward Euler, Runge-Kutta 2 Midpoint Method, and Runge-Kutta 4th Order blow up. Semi-Implicit Euler and Velocity Verlet are stable but not accurate.
To see N-body patterns, refer to the Particle Systems section.