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Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations

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T. D. BuiAuthors Info & Claims

Journal of the ACM (JACM), Volume 26, Issue 3

Pages 483 - 493

https://doi.org/10.1145/322139.322147

Published: 01 July 1979 Publication History

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References

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ALLEN, R H, AND POTTLE, C Stable integration methods for electronic orcutt analysis with widely separated time constants, Proc Sixth Annual Allerton Conf on Clrcult and System Theory, U of llhnots at Urbana- Champaign, Urbana, I11, T Trick and R T Chlen, Eds, 1966, pp 311-320

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BICKART, T A An efficient solution process for implicit Runge-Kutta methods SIAM d Numer Anal 14, 6 (Dec 1977), 1022-1027

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BRANDON, D M A new single-step implicit integration algorithm with A-stablhty and improved accuracy S:mulat:on 23, 1 (July 1974), 17-29

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BuI, T D Errata and comments on a paper by J R Cash J A CM 24, 4 (Oct 1977), 623

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Btsr, T D, AND GHADERPANAH, S Modified Richardson extrapolation scheme for error estimate in tmphcit Runge-Kutta procedures for stiff systems of ordinary differential equations Proc Seventh Manitoba Conf on Numerical Math and Comptng, Utlhtas Mathematlca Pub, lnc, Winnipeg, Mamtoba, Canada, 1977, pp 251-268

[6]

BuI, T D, LELrNG, K V, AND BuI, T R New developments in computer techniques for stiff differential equations Proc Sixth Canadian Congress of Appl Mech, U of British Columbia, Vancouver, Brmsh Columbia, Canada, 1977, pp 1035-1037

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BURRAGE, K A special family of methods for solving surf differential equations Res Rep No I10, Dept of Mathematics, U of Auckland, Auckland, New Zealand, May 1977

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BUTCHER, J C Imphot Runge-Kutta processes Math Comput 18 (1964), 50-64

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BUTCHER, J C On the lmplementauon of lmphcit Runge-Kutta methods BIT 16 (1976), 237-240

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CALAHAN, D A stable accurate method for the numerical integration of nonhnear systems Proc IEEE 56 (April 1968), 744

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CASH, J R SemHmphcR Runge-Kutta procedures with error estimates for the numerical integration of stiff systems of ordinary differential equations J A CM 23, 3 (July 1976), 455--460

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DAHLQUIST, G G A special stability problem for linear multlstep methods BIT 3 (1963), 27-43

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EHLE, B L High order A-stable methods for the numerical solution of differential equations BIT 8 (1968), 276-278

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HAINES, C F Imphclt integration processes wRh error estimates for the numerical solution of differential equations Computer J 12 (1968), 183-187

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LAMBERT, J D Computational Methods tn Ordinary D~fferenttal Equations Wiley, New York, 1973

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LINDBERG, B On smoothmg and extrapolation for the trapezoidal rule BIT 11 (1971), 29-52

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NORSETT, S P Semi-explicit Runge-Kutta methods Math and Computation Rep 6/74, Dept of Math., U of Trondhelm, Trondheim, Norway, 1974

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PICEL, Z Block one-step methods with free parameters for numerical integration ofstlffordmary differential equattons Ph D Th, Syracuse U, Syracuse, N Y. 1975

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ROSENaROCK, H H Some general ~mpllctt processes for the numerical solution of differential equations Computer J 5 (1963), 329-330

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WOLFBRANDT, A A study of Rosenbrock processes w~th respect to order condmons and st~ff stabdtty Res Rep No 77 01, Dept of Comptr Sc~, U of Goteborg, Goteborg, Sweden, 1977

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Caplan RJohnston CDaldoff LLinker J(2024)Advancing parabolic operators in thermodynamic MHD models II: Evaluating a Practical Time Step Limit for Unconditionally Stable MethodsJournal of Physics: Conference Series10.1088/1742-6596/2742/1/0120202742:1(012020)Online publication date: 1-Apr-2024
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Beznogov MNovak JPage DRaduta A(2023)Standard Cooling of Rapidly Rotating Isolated Neutron Stars in 2DThe Astrophysical Journal10.3847/1538-4357/ac9eb7942:2(72)Online publication date: 12-Jan-2023
https://doi.org/10.3847/1538-4357/ac9eb7
Griese MPawlik TSchulte TMaas J(2016)Electrodynamical modelling of bidirectional fuel cell systems for HIL simulations of combined grid systems2016 10th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG)10.1109/CPE.2016.7544182(186-191)Online publication date: Jun-2016
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Index Terms

Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 26, Issue 3

july 1979

217 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/322139

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Copyright © 1979 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1979

Published in JACM Volume 26, Issue 3

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Cited By

Caplan RJohnston CDaldoff LLinker J(2024)Advancing parabolic operators in thermodynamic MHD models II: Evaluating a Practical Time Step Limit for Unconditionally Stable MethodsJournal of Physics: Conference Series10.1088/1742-6596/2742/1/0120202742:1(012020)Online publication date: 1-Apr-2024
https://doi.org/10.1088/1742-6596/2742/1/012020
Beznogov MNovak JPage DRaduta A(2023)Standard Cooling of Rapidly Rotating Isolated Neutron Stars in 2DThe Astrophysical Journal10.3847/1538-4357/ac9eb7942:2(72)Online publication date: 12-Jan-2023
https://doi.org/10.3847/1538-4357/ac9eb7
Griese MPawlik TSchulte TMaas J(2016)Electrodynamical modelling of bidirectional fuel cell systems for HIL simulations of combined grid systems2016 10th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG)10.1109/CPE.2016.7544182(186-191)Online publication date: Jun-2016
https://doi.org/10.1109/CPE.2016.7544182
Verma AVerma L(2015)Higher order time integration formula with application on Burgers’ equationInternational Journal of Computer Mathematics10.1080/00207160.2014.90903292:4(756-771)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1080/00207160.2014.909032
KIM JELANGOVAN R(2013)An efficient numerical computation scheme for stiff equations of droplet trajectories24th Aerospace Sciences Meeting10.2514/6.1986-407Online publication date: 18-Feb-2013
https://doi.org/10.2514/6.1986-407
de la Cruz HBiscay RJimenez JCarbonell F(2013)Local Linearization—Runge–Kutta methods: A class of A-stable explicit integrators for dynamical systemsMathematical and Computer Modelling10.1016/j.mcm.2012.08.01157:3-4(720-740)Online publication date: Feb-2013
https://doi.org/10.1016/j.mcm.2012.08.011
Savant GBerger R(2012)Adaptive Time Stepping–Operator Splitting Strategy to Couple Implicit Numerical Hydrodynamic and Water Quality CodesJournal of Environmental Engineering10.1061/(ASCE)EE.1943-7870.0000547138:9(979-984)Online publication date: Sep-2012
https://doi.org/10.1061/(ASCE)EE.1943-7870.0000547
Georgiev KZlatev Z(2011)Implementation of sparse matrix algorithms in an advection-diffusion-chemistry moduleJournal of Computational and Applied Mathematics10.1016/j.cam.2011.07.026236:3(342-353)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1016/j.cam.2011.07.026
Zou RGhosh A(2006)Automated sensitivity analysis of stiff biochemical systems using a fourth-order adaptive step size Rosenbrock integration methodIEE Proceedings - Systems Biology10.1049/ip-syb:20050058153:2(79)Online publication date: 2006
https://doi.org/10.1049/ip-syb:20050058
Shampine L(2006)Global error estimation for stiff ODEsNumerical Analysis10.1007/BFb0099523(159-168)Online publication date: 15-Nov-2006
https://doi.org/10.1007/BFb0099523
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