Euler vs. 4th-order Runge-Kutta

[oswaler]

I need to solve some differential equations for a system of millions of particles (molecular dynamics if that means anything to anyone - and yes I know MD has been done but for our purposes we have to start from scratch). In looking at various methods of implementing this, I have tried EUler and I've tried RK4. Theoretically Euler should be much less accurate than RK4 but when I tried writing routines around DEs I already had solutions for using both I found that Euler executed in roughly half the time RK4 did and was actually sometimes more accurate than RK4. I have only run them for a couple of equations so far and I know certain methods can be well suited for certain types of equations. Does anybody have any opinions on Euler vs. RK4 or have any other preferred method that has worked well in practical implementation?

Thanks - Eric

[twanvl]

According to the course on this stuff I am currently taking, Euler integration is prefered for MD, because it is a lot faster. The time steps in these simulations are usually very small, so the error is small as well.