The first application is Euler Integrator with step size 0.1. Red lines are precise solution. The blue line are the error
produced by the integrator.
Euler Integrator
The second application is Runge-Kutta order 4 Integrator with step size 0.1. Error is nearly invisible.
RK4 Integrator
The third application is simulation of pendulum with periodic forcing using Runge-Kutta order 4 Integrator.
Pendulum