This example demonstrates various ways in which you can use a solver node to transform an object based on ordinary differential equations.

There are 6 different solvers in this example. There is also the exact answer as a point of reference. The solvers are numerical methods that solve the following coupled Ordinary Differential Equations with initial conditions:

x' = y ; x(0) = 1
y' = -x ; y(0) = 0

The numerical methods for Ordinary Differential Equations are: Forward Euler, Runge-Kutta Second Order, Runge-Kutta Third Order, Runge-Kutta Fourth Order, and Parker-Sochacki solved two ways. In one version, Parker-Sochacki is hard coded at order 5. In another version Parker-Sochacki is written in a for loop where the order can be adjusted by the user.