Comparison (34C-59) of numerical ∫ algorithm

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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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