possible issue in the relative step error computations in case of variable step-size integrators

[princemahajan]

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.

[jacobwilliams]

I need to look and see what I did... my idea was you could have different step size selection logic depending on the options you set.

[princemahajan]

Yes you can. I just wanted to confirm that this is a correct local error computation formula that uses the second power of h and not first. Did you find this formula in some paper?