A comparison of three computer algebra systems for the solution of a problem in hydrodynamic lubrication

Abstract

With the plethora of computer algebra languages and systems available today, it is useful to compare some of these languages when a research problem highlights differences between them. The problem that we have been studying arises in the field of hydrodynamic lubrication theory, and provides a moderate-to-severe test of the capabilities of a computer algebra system. The problem was solved in part by Jeffrey & Onishi [1984] using CAMAL (Fitch, 1983) on an IBM 3081 at Cambridge University. Further calculations were needed, however, and CAMAL was no longer available, so since muMATH (Stoutemeyer & Rich, 1983) running on various IBM PC compatibles and later Maple (Char et al , 1985) running on a VAX 8550 under VMS version 4.5 were available, it was natural to try these out on the problem. The authors are of course aware of the difficulty in comparing languages running on machines with very widely differing speeds and memory, and the reader is asked to keep this firmly in mind when seeing any run times quoted. What follows is a brief description of the problem, here taken out of its original context and used as a test problem. For a discussion of the problem concentrating on the fluid mechanical theory see Corless & Jeffrey (1988a). For a brief description of the complete solution obtained with Maple, see Corless & Jeffrey (1988b).