Recently when I was solving a system of ODEs using runge-Kutta method , I got much different results when I transformed the variables from spherical coordinates ($r$ and $\theta$ ) to cylindrical coordinates($\rho$ and $z$) and solved it again.
(no need to mention that
Only the results obtained using second system (in cylindrical_ which only contained polynomials of variables and didn't have fractions of variables_) were in agreement with published results.
Now, I wonder if there is a simple rule to determine the best form of a system to solve using numerical algorithms such as runge_kutta.(for example , something like :division of variables is better to be avoided) (or maybe this disagreement was a mistake somewhere in my calculations? (i.e. such a difference in results is impossible))