Opinions on matters connected with the evaluation of programs and methods for integrating ordinary differential equations

ABSTRACT

Eighty-seven items which might be considered in the evaluation of programs for solving differential equations are listed, and ten experts in the field give their opinions on the importance of each item.

REFERENCES

• 1: Clark, Nancy W. A Study of Some Numerical Methods for the Integration of Systems of First-Order Ordinary Differential Equations. Report # ANL-7428, Argonne National Laboratory, Argonne, Illinois, March 1968.
• 2: Crane, P. C. and Fox, P. A. A Comparitive Study of Computer Programs for Integrating Differential Equations. Bell Telephone Laboratories Numerical Mathematics Computer Programs, Library One - Basic Routines for General Use, Vol. 2, Issue 2 (1969).
• 3: Greenspan, H.; Hafner, W.; and Ribaric, M. On Varying Stepsize in Numerical Integration of First Order Differential Equations. <u>Numerische Math.</u> 7 (1965), 286--291.
• 4: Henrici, Peter. <u>Discrete Variable Methods in Ordinary Differential Equations.</u> Wiley, New York, 1962.
• 5: Hull, T. E.; Enright, W. H.; Fellen, B. M.; and Sedgwick, A. E. Comparing Numerical Methods for Ordinary Differential Equations. University of Toronto Department of Computer Science Report No. 29, August 1971. (To appear in <u>SIAM Journal on Numerical Analysis</u>, December 1972).
• 6: Klopfenstein, R. W. Numerical Differentiation Formulas for Stiff Systems of Ordinary Differential Equations. <u>RCA Review 32</u> (1971), 447--462.
• 7: Krogh, F. T. On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations. JPL Internal Document, Section 914 TM No. 217, (revised), Jet Propulsion Laboratory, Pasadena, California, October 1970.
• 8: Krogh, F. T. An Integrator Design. JPL TM 33-479, Jet Propulsion Laboratory, Pasadena, California., May 1971.
• 9: Fred T. Krogh, A plea for tolerance in the evaluation of numerical methods and mathematical software, ACM SIGNUM Newsletter, v.6 n.3, p.7-8, November 1971 [doi>10.1145/1052623.1052624]