Comparison (34C-59) of numerical ∫ algorithm

[SlideRule]

An excerpt from NUMERICAL RELATIONSHIPS FOR TEMPERATURE INTEGRALS WITH TEMPERATURE DEPENDENT FREQUENCY FACTORS, Thermochimica Acta, 54 (1982), pg, 214

METHODS
  Evaluations of temperature integrals for m = 0, 1/2, 1, 3/2, and 2 were previously carried out using a Texas Instruments TI-59 Programmable calculator. In this work, the integrals for m = -1/2, -1, -3/2, and -2 were evaluated using a Hewlett-Packard HP-34C calculator employing the three-digit scientific notation accuracy (f SC1 3). This instrument has a built-in numerical integration algorithm that calls as a subroutine the previously entered sequence to evaluate the function being integrated. The HP-34C was used because the algorithm that it uses provides greater accuracy in a shorter time than does the Master Library Simpson’s rule program of the TI-59. For example, the three-digit scientific notation format with the HP-34C gives a result of -logI = 15.38760326 in about 2.6 min for the case with m = 0, E = 30 kcal mole^-1, and T = 400 K. The TI-59 requires a 300 subinterval Simpson’s rule computation and requires about 8.4 min to provide a result this close to the actual value of 15.38760423. Consequently, the HP-34C enables a greater accuracy to be obtained in a shorter computing time and it was used for all the numerical integrations in this work. As is true with the TI-59, a greater accuracy can be obtained, but at the sacrifice of computing speed. Linear regression was carried out as previously described.

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[Johnh]

That's interesting indeed! I had a TI58, and now an HP15c-ce, which I understand has an integration method similar to the 34. It's definitely much more sophisticated, and so also faster to reach a given accuracy though it's hard to test physically using modern hardware and sims.

But at the time, 1979 and though my engineering studies, I appreciated the TI use of Simpson's rule because we had been taught it in high-school maths in the UK. So knowing more about what's inside the black box gave me confidence in using it appropriately, despite limitations.

[Steve Simpkin]

The Aug 1980 issue of HP Journal magazine has detailed information on the Numerical Integration feature of the HP-34C (page 23). This article was written by Professor William Kahan who developed the Solve and Integration algorithms for the HP-34C. A PDF of this issue is available here:
http://hparchive.com/Journals/HPJ-1980-08.pdf

There is a really interesting story behind the development of the HP-34C. Professor William Kahan, who worked as a consultant for HP, came up with an algorithm for a numeric solver and really wanted HP to implement it in a calculator. The problem was that HP marketing had no interest in making a model with a solver. Their marketing studies convinced them that their customers did not want a calculator with a "Solve" key. Professor Kahan kept bringing this subject up with Stan Minz, the person in charge of one of the HP calculator development groups. Finally Stan said if you can create an algorithm that will fit in a calculator that solves numeric integration problems, I will incorporate your Solve function into that calculator. That is just what professor Kahan did. Even after HP committed resources to making the HP-34C, HP management did not want to fully document the new Solve/integration functionality. The full story is very entertaining as is the story behind the development of the HP-15C.

Professor Kahan's full oral history PDF document can be found at the following link. The discussion of the HP-34C starts on page 152.
https://drive.google.com/file/d/1Jlg9EWQ...zwcol/edit