Single Spring in 1D:

Single Spring in 2D:

Double Spring in 1D:

Double Spring in 2D:

This section is designed to be the first known research steps at applying the Parker-Sochacki method to the Ordinary Differential Equations to different types of springs: A single spring in 1 and 2 dimensions and a double spring in 1 and 2 dimensions. The higher accuracy of the Parker-Sochacki method led to larger time steps and more flexibility with constants like damping. This shows promise that Parker-Sochacki would do well on a mass-spring system when applied to hair or cloth simulations. There is also a post that compares results between Parker-Sochacki 4th Order and Runge-Kutta 4th Order.

Single Spring in 1 Dimension :

Single Spring in 2 Dimensions:

Double Spring in 1 Dimension:

Double Spring in 2 Dimensions:

Parker-Sochacki vs Runge-Kutta in terms of speed: