I have devised a numerical algorithm that solves an equation of type
$$\dot{A} = f(A) \, ,$$
where $A$ is always a symplectic matrix. My algorithm respects this in the sense that, for all $A$ obtained numerically, we have
$$A^T J A = J \quad \text{and, as a consequence,} \quad \det(A) = 1 \, ,$$
where $J$ is the symplectic matrix. Since my algorithm always generates symplectic matrices and there are no exact solutions available for comparison, how can I estimate its error? Other routines that solve this equation do not provide symplectic solutions and deviations are usually searched for using how much they deviate from symplecticity, which is not applicable in my case.