rate constants determination: from ODEs solving v.s. numerical integration

[FanCG]

Again in the book "chemical kinetics with maple and mathcad", chapter 4 introduces different ways for rate constants determination.

Take figure 4.8 as an example (corresponding attached file is "Fig_4_08_PineneIsomerization_InvTask_MC14" ), numerical integration method is used searching rate constants:

but i think that solving ODEs is more direct and general than integration method, so I solve the problem with ODEsolve method:

Both methods looks good enough, but differential method results are closer to that of DYANFIT than for integral method.

But differential method seems much more initial-condition sensitive than integral method, e.g. if guess values of k1--k4 are all set to 1, the calculation will be very time-consuming. and I dont know how to improve this situation.

Does anybody give any suggestions on "lowering/ reducing" the initial - condition sensitivity of differential method?

[HarveyHensley]

For parameter estimation, all parameters should be scaled to the same order of magnitude and then you try guesses for two orders of magnitude surrounding the expected values.

[AlanStevens · Accepted solution]

Try basing your initial guesses on the information available to you from the basic data and, where possible, the form of the equations. See attached.

Alan

Improved file attached

[FanCG]

Thanks. Alan

your method is very interesting, time-saving and skillful than mine. I appreciate very much. Now I got three ways of solving the problem, lol.

by the way, I think your answer is more educational than practical, coz the reaction orders are all integers, and this is not very often in engineering practice.

thanks a lot again for your very detailed answer to my question

[ValeryOchkov]

Thanks to all for the interesting to the book http://twt.mpei.ac.ru/TTHB/New-Chem-Kin/En-Ru-book.html

Now we try to solve book's problems in Prime with units - mole, L, sec etc.

This discussion is very usefull for the second edition of the book.