Apparently it's O(t^2). I've just realised I don't know what that means. What is the expression for the expected error in the position for the velocity verlet algorithm? Related to the timestep, but in what way? I keep reading about local and global error but don't know what that means.
I just wanted to know the expected relationship between error and timestep for the position, but can't find it on google. Should it be proportional to 1/t^2? Or something like that?
With a time step h, the error at time t for moderate values of t is O(t·h²), meaning that the error at any fixed time falls quadratically with the step size and the coefficient of this h² grows, first almost linearly, later exponentially, with t.
The local error is the discretization error, the difference of the exact solution versus one time step of the integration method. The global error is the compound error of all local errors. In practical numerical application, the local error gets an additional random term accounting for the floating point truncations of arithmetic operations.
