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RK4

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I seen a Schultz saying, about RK4, "it acts as a low pass filter". Considering we didn't have a detailed talk about a somehow difficult problem for a while (on this forum), it might be nice to reopen a debate about integrators. So a few questions. (If you have a hard numbers for behavior of other integrators, you might post them as well.)
  • Is problem with RK4 acting as a low pass filter, shared by a symplectic version of the algorithm?
  • Could you provide some on line accessible reference for misbehaviors of RK4?
  • What was your experience with bad behavior of the RK4?
  • Is there some problem that is extraordinally bad for RK4?
  • Edgeworth said it's bad idea to use for 3D problem a version of RK4 algorithm that wasn't designed for 3D space. How large would be a difference?
  • How many steps per orbit would you need for 2 body problem, if you'd like a stable orbit?
  • For 3 body?
  • How large would be a difference from a real solution? Let's say you'd use 2* of minimal amount of steps, and 50 steps per orbit.
  • This might be a somehow nice start. BTW I don't use RK4, I use a sympletic 6th order algorithm, that is braindead to implement, so I don't have experience with this type of integrator. (So don't expect I'd participate too actively in this thread.)

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    Can you explain your questions in simpler terms? They look interesting...

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