Thread: RK4, Euler, and computer simulations

Just the other day I bought a computer game called "Universe Sandbox". It basically a $10 physics engine. I enjoy it very much. Theres this one thing in the Options menu where I can switch between "Normal" and "Accurate" modes. The difference being that in "Normal" mode it uses Euler math, and in "Accurate" mode ituses RK4. I know nothing about either. So here's my question.

What is the difference between the Euler and RK4? The game just says Euler is quicker. I assume that means Euler uses a shorter formula. Is that all
there is to it?

I tried looking on wikipedia but the articles they have on Euler and RK4 get intense pretty fast. I was hoping someone could give me a layman's breakdown.

Most physical processes are described by differential equations. To solve the differential equation, you can solve it explicitly. In the case gravity and two masses, the solution is a conic section. For planets, the solution is approximated by an ellipse in a lot of models. Euler and RK4 are both Runge-Kutta methods that "jump" from one time to the next in small steps. The error in doing this is usually small, but it can build up over time. RK4 does a better job of controlling those errors than Euler, but it's more complicated, and takes longer, as you suspected.

Linky.

Wikipedia can be your friend...

It can also be confusing.