If you want to see the folly of RK4, give it something like a ball bouncing and watch as it bounces slightly higher each time. Subtle at first, but trust me its

If you want to see the folly of RK4, give it something like a ball bouncing and watch as it bounces slightly higher each time. Subtle at first, but trust me its there. The comment above you is right. If you have conservation of energy and want to keep it that way, use verlet. Edit: before anyone calls me out on this, the same trick also works when there's no discontinuity in the force function vis a vis collision with the floor. Planetary motion also drifts out of simple orbits. I just picked the ball bouncing because its a more amusing visual.