# What are the Integration methods for non-separable hamiltonian?

Interested in numerically solving non-separable Hamiltonians. The Wolfram documentation states that the symplectic schemes can only be implemented for separable Hamiltonians of the form

$$H(p,q) = T(p) + V(q).$$

Even this, I believe has some bugs which are discussed here. Now my thoughts are to simply let Mathematica do the leg work for e.g. generating the coefficients of the butcher tableau etc. etc. and then use this in my "own" designed integrator. Basically sidestepping the limitation of checking whether a Hamiltonian is separable or not...

Question

• Is there an alternative method to what I have suggested?