rkdp85 Module Procedure

Note

The error estimate is the one from DOP853, which combines a 5th and a 3rd order estimate. By default, this is done for each component: $err = err_5 |err_5| / \sqrt{err_5^2 + 0.01 err_3^2}$. This behaves like $O(h^8)$, so it is consistent with the error of the 8th order solution (using only the 5th order estimate would overestimate it, resulting in steps that are smaller than necessary). With the error_combination=2 option of the stepsize_class, it is done as in DOP853, using the norms of the two scaled error estimates: $err = err_5 E_5 / \sqrt{E_5^2 + 0.01 E_3^2}$, where $E_i = ||err_i/tol||$ (so the norm of the scaled error is $E_5^2 / \sqrt{E_5^2 + 0.01 E_3^2}$, as in DOP853).