|Free42 Integration "Bug"|
Message #1 Posted by Les Wright on 4 Jan 2007, 1:36 p.m.
Lovers of Thomas Okken's excellent simulator may find this interesting. I have let Thomas know about it so he can refine as he wishes, but in the meantime there is an easy workaround.
I have discovered that in Free42 the ACC parameter for the integrator actually is treated as the target ABSOLUTE error specified by the user, whereas in the actual calculator it is supposed to be the relative error (cf. Owner's Manual p. 203). This gives misleading results when computing integrals where the magnitudes are quite small.
For example, when computing the integral of exp(-1/x^2)/x^2 from 0 to 0.1, using an ACC of, say, 0.0001 results in a pretty good result on the calculator but a bad result in Free42. However, if one specifies a desired absolute error (the integral result is of the order of 1.9e-45, so, say 1e-50), you get a more sensible result in Free42. But use such a tiny value for ACC on the 42s, of course the thing will never converge.
I have let Thomas know about this since I know he is keen to make Free42 a completely faithful simulation of the real calculator.