Question

How accurate will a simulation of the double pendulum using the RK4 method be?

Answer 1

I ask because I have recently been reading about issues with the RK4 method in problems that require the conservation of the Hamiltonian. Since RK4 is not a symplectic integrator, I assume that the simulation will quickly diverge from the correct solution. That said, in my tests the general solution seems to be roughly in line with the expected results that I have found in a couple of papers. Does anyone have any experience with this - is the divergence something to be worried about, and over what rough timescale can we expect this to play an important role in the accuracy of the simulation?

One related question is what symplectic integrators could I use to replace the RK4 method I've been using?

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