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

Editor: Johyn R. Rice Author:

L. F. ShampineAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 3, Issue 1

Pages 44 - 53

https://doi.org/10.1145/355719.355722

Published: 01 March 1977 Publication History

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References

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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.

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KROGH, F.T. On testing a subroutine for the numerical integration of ordinary differential equations. J. ACM ~0, 4 (Oct. 1973), 545-562.

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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.

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SHAMPIN~, L.F. Limiting precision in differential equation solvers. Math. Comput. $8 (1974), 141-144.

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SHAMPINE, L.F., AND ALLEN, R.C. Numerical Computing: An Introduction. W.B. Saunders, Philadelphia, Pa., 1973.

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SHAMPINE, L.F., AND GORDON, M.K. Computer Solution of Ordinary Differential Equations: The Initial Value Problem. W. H. Freeman, San Francisco, Calif., 1975.

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SHAM~INE, L.F., AND GORDON, M.K. Typical problems for stiff differential equations. SIGNUM Newsletter (ACM) I0 (1975), 41.

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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.

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https://doi.org/10.1515/math-2018-0022
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Index Terms

Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
  2. Mathematical software

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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

Editor:
Johyn R. Rice

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 1977

Published in TOMS Volume 3, Issue 1

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Crawford TKumar ABazanté ADi Remigio R(2019)Reduced‐scaling coupled cluster response theory: Challenges and opportunitiesWIREs Computational Molecular Science10.1002/wcms.14069:4Online publication date: 8-Jan-2019
https://doi.org/10.1002/wcms.1406
Bu S(2018)Time parallelization scheme with an adaptive time step size for solving stiff initial value problemsOpen Mathematics10.1515/math-2018-002216:1(210-218)Online publication date: 20-Mar-2018
https://doi.org/10.1515/math-2018-0022
Heimlich ASilva FMartinez A(2018)Fast and accurate GPU PWR depletion calculationAnnals of Nuclear Energy10.1016/j.anucene.2018.02.045117(165-174)Online publication date: Jul-2018
https://doi.org/10.1016/j.anucene.2018.02.045
Gleim TKuhl D(2018)Electromagnetic Analysis Using High-Order Numerical Schemes in Space and TimeArchives of Computational Methods in Engineering10.1007/s11831-017-9249-9Online publication date: 5-Jan-2018
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Emagbetere EOluwole OSalau T(2017)Comparative Study of Matlab ODE Solvers for the Korakianitis and Shi ModelBulletin of Mathematical Sciences and Applications10.18052/www.scipress.com/BMSA.19.3119(31-44)Online publication date: Aug-2017
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Dallas SMachairas KPapadopoulos E(2017)A Comparison of Ordinary Differential Equation Solvers for Dynamical Systems With ImpactsJournal of Computational and Nonlinear Dynamics10.1115/1.403707412:6(061016)Online publication date: 7-Sep-2017
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Trivedi KBobbio A(2017)State-Space Models with Non-Exponential DistributionsReliability and Availability Engineering10.1017/9781316163047.017(487-488)Online publication date: 30-Aug-2017
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Diagnosing Stiffness for Runge–Kutta Methods

Runge-Kutta discontinuous Galerkin method using WENO limiters II

Exponential Runge--Kutta methods for the Schrödinger equation

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