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I am not 100% on this because you are using slightly different step size computation formulae. In step computation routine for each integrator (variable-step), you compute the step errors as this
xerr = sum (h*e(i)*F(i))
Then in step size computation routine (rklib_module.F90) , the max_err is computed like this
max_err = abs(xerr*h/tol)
So you are saying that step error for your integrators is O(h^2) and not O(h). Is that correct? Since you have included so many different algorithms so it may be you are using a different step size formulae than what is more typically used (esp. with DOP54 and DOP853). In case your formula is correct then you can close this issue.
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