Two FORTRAN packages for assessing initial value methods

ABSTRACT

We present a discussion and description of a collection of FORTRAN routines designed to aid in the assessment of initial value methods for ordinary differential equations. Although the overall design characteristics are similar to those of earlier testing packages [2,6] that were used for the comparison of methods [5,7], the details and objectives of the current collection are quite different. Our principal objective is the development of testing tools that can be used to assess the efficiency and reliability of a standard numerical method without requiring significant modifications to the method and without the tools themselves affecting the performance of the method.

REFERENCES

• 1: ADDISON, C.A. Implementing a stiff method based upon the second derivative formulas. Rep. No. 130, Dept. of Computer Science and Technology, Univ. of Toronto, Toronto, 1980.
• 2: BEDET, R. A., ENRIGHT, W. H., AND HULL, T.E. Stiff ODEs. Rep. No. 81, Dept. of Computer Science and Technology, University of Toronto, Toronto, 1975.
• 3: ENRIGHT, W.H. Using a testing package for automatics assessment of numerical methods for ODEs. In Per{ormance Evaluation of Numerical So{tware, L. D. Fosdick, Ed. North-Holland, Amsterdam, 1979, pp. 199-212.
• 4: ENRIGHT, W. H., AND HULL, T. E. Comparing numerical methods for the solution of stiff systems of ODEs arising in chemistry. In Numerical Methods/or Di{/erential Systems, L. Lapidus and W. E. Schiesser, Eds. Academic Press, Orlando, Fla., 1976, pp. 45-67.
• 5: ENRIGHT, W. H., HULL, T. E., AND LINDBERG, B. Comparing numerical methods for stiff systems of ODEs. BIT 15 (1975), 10-48.
• 6: HALL, G., ENRIGHT, W. H., HULL, T. E., AND SEDGWICK, A. E. DETEST: A program for comparing numerical methods for ordinary differential equations. Rep. No. 60, Dept. of Computer Science and Technology, Univ. of Toronto, Toronto, 1973.
• 7: HULL, T. E., ENRIGHT, W. H., FELLEN, B. M., AND SEDGWICK, A.E. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9, 4 (1972), 603-637.
• 8: HULL, T. E., ENRIGHT, W. H., AND JACKSON, K.R. User's guide for DVERK--a subroutine for solving nonstiff ODEs. Rep. No. 100, Dept. of Computer Science and Technology, Univ. of Toronto, Toronto, 1976.
• 9: Lawrence F. Shampine, Evaluation of a Test Set for Stiff ODE Solvers, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.409-420, Dec. 1981 [doi>10.1145/355972.355973]
• 10: ZONNEV~LD, J.A. Automatic numerical integration. Mathematical Center Tracts 8, Mathematisch Centrum, Amsterdam, 1964.

INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

General Terms:
Algorithms, Performance, Reliability