I am using dodesol_mk52lfn as a replacement for the Gear numerical integrator in the IMSL. dodesol_mk52lfn has a tolerance input argument, ep, which I do not understand. dodesol_mk52lfn output matches IMSL quite well with ep on the order of 0.1 to 1.0, whereas it seems that this argument ought to be on the order of 1e-6. For instance, the example problem in the documentation uses ep=1e-6 and says this produces accuracy of "about 5%".
ep DOUBLE PRECISION
(input) Relative error tolerance, which must be small enough. The code cannot ensure the requested accuracy for ep<1.d-9. This parameter is used to control the step size.
But my question is about the MKL routine, not about the IMSL routine. I need help with the MKL routine. What the documentation says about the "relative error tolerance" is not consistent with the results I get using the routine. Is it possible the "relative error" is defined in a non-standard way?