The stiff integrators in the NAG library

ABSTRACT

We have designed a new generation of stiff ordinary differential equation (ODE) solvers for the NAG LIbrary. They replace existing routines which are functionally inferior and have much less user-friendly interfaces. The redesign provides:(i) continuity and stability for users of NAG stiff solvers;(ii) general simplification of interfaces;(iii) new functionality - solving implicit and differential/algebraic systems;(iv) flexibly structured open ended software (based on implicit ODE methods) so that adding new integration methods is a simple matter;(v) a design which facilitates using the solvers from other packages;(vi) an interface which permits the solvers to be used at the "assembly language" level in packages written in more "robust" languages than Fortran77 (for example ADA).

REFERENCES

• 1: Berzins, M., Brankin, R. W., and Gladwell, I. (1987) Design of the Stiff Integrators in the NAG Library, Num. Anal. Rept. 143, Dept. of Mathematics, University of Manchester.
• 2: Berzins, M., Dew, P. M. and Furzeland, R. M. (1986) Developing PDE Software Using the Method of Lines and Differential-Algebraic Integrators. (Highlighted talk presented at 1986 ODE conference, Albuquerque) Rept. 220, Dept. Comp. Stud., University of Leeds.
• 3: Berzins, M. and Furzeland, R. M. (1985) A User's Manual for Sprint --- A Versatile Software Package for Solving Systems of Algebraic, Ordinary and Partial Differential Equations, Rept. TNER 85.058, Shell Research Ltd.
• 4: Berzins, M. and Furzeland, R. M. (1986) A type insensitive method for the solution of stiff and non-stiff differential equations, Rept. 204, Dept. Comp. Stud., University of Leeds.
• 5: Enright, W. H., Jackson, K. R., Norsett, S. P. and Thomsen, P. G. (1986) Effective Solution of Discontinuous IVP's using a Runge-Kutta Formula Pair with Interpolants, Num. Anal. Rept. 113, University of Manchester.
• 6: Ian Gladwell, Initial Value Routines in the NAG Library, ACM Transactions on Mathematical Software (TOMS), v.5 n.4, p.386-400, Dec. 1979 [doi>10.1145/355853.355856]
• 7: I. Gladwell , L. F. Shampine , R. W. Brankin, Automatic selection of the initial step size for an ODE solver, Journal of Computational and Applied Mathematics, v.18 n.2, p.175-192, May 1987 [doi>10.1016/0377-0427(87)90015-X]
• 8: Hindmarsh, A. C. (1980) LSODE and LSODI, Two New Initial Value Ordinary Differential Equation Solvers, <i>SIGNUM</i>, <b>15</b>, 10--11.
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• 10: Hindmarsh, A. C. (1978) GEAR: Ordinary Differential Equation Solver, Rept. UCID-30001, Rev.3, Lawrence Livermore Lab., Livermore, CA.
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Stiff equations

Additional Classification:
  G. Mathematics of Computing

General Terms:
Design, Theory