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Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods

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Published:01 March 1977Publication History
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References

  1. 1 BJUREL, G., DAHLQUIST, G., LINDBERG, B., LINDE, S., AND ODIN, L. Survey of stiff ordinary differential equations. Rep. No. NA 70.11, Dep. Information Processing, Royal Inst. Technology, Stockholm, Sweden, 1970.Google ScholarGoogle Scholar
  2. 2 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 (1972), 603-637.Google ScholarGoogle Scholar
  3. 3 KROGH, F.T. On testing a subroutine for the numerical integration of ordinary differential equations. J. ACM ~0, 4 (Oct. 1973), 545-562. Google ScholarGoogle Scholar
  4. 4 SHAMPINE, L.F. Stiffness and non-stiff differential equation solvers. In Numerische Behandlung yon Different~algleichungen, L. Collatz, Ed., Int. Series Numer. Math. 27, Birkhauser, Basel, Switzerland, 1975, pp. 287-301.Google ScholarGoogle Scholar
  5. 5 SHAMPIN~, L.F. Limiting precision in differential equation solvers. Math. Comput. $8 (1974), 141-144.Google ScholarGoogle Scholar
  6. 6 SHAMPINE, L.F., AND ALLEN, R.C. Numerical Computing: An Introduction. W.B. Saunders, Philadelphia, Pa., 1973. Google ScholarGoogle Scholar
  7. 7 SHAMPINE, L.F., AND GORDON, M.K. Computer Solution of Ordinary Differential Equations: The Initial Value Problem. W. H. Freeman, San Francisco, Calif., 1975.Google ScholarGoogle Scholar
  8. 8 SHAM~INE, L.F., AND GORDON, M.K. Typical problems for stiff differential equations. SIGNUM Newsletter (ACM) I0 (1975), 41. Google ScholarGoogle Scholar
  9. 9 SHAMPINE, L.F., WATTS, H.A., AND DAVENPORT, S.M. Solving non-stiff ordinary differential equations--the state of the art. SIAM Rev. 18 (1976), 376-411.Google ScholarGoogle Scholar

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  1. Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods

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        cover image ACM Transactions on Mathematical Software
        ACM Transactions on Mathematical Software  Volume 3, Issue 1
        March 1977
        112 pages
        ISSN:0098-3500
        EISSN:1557-7295
        DOI:10.1145/355719
        Issue’s Table of Contents

        Copyright © 1977 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 March 1977
        Published in toms Volume 3, Issue 1

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