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A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations

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J. R. CashAuthors Info & Claims

Journal of the ACM (JACM), Volume 22, Issue 4

Pages 504 - 511

https://doi.org/10.1145/321906.321915

Published: 01 October 1975 Publication History

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References

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Cited By

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Aihie IOkuonghae R(2024)A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEsEarthline Journal of Mathematical Sciences10.34198/ejms.14324.565588(565-588)Online publication date: 4-Apr-2024
https://doi.org/10.34198/ejms.14324.565588
Noren H(2023)Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta MethodsGeometric Science of Information10.1007/978-3-031-38271-0_55(552-559)Online publication date: 30-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-38271-0_55
Olatunji PIkhile MOkuonghae R(2021)Nested Second Derivative Two-Step Runge–Kutta MethodsInternational Journal of Applied and Computational Mathematics10.1007/s40819-021-01169-17:6Online publication date: 22-Nov-2021
https://doi.org/10.1007/s40819-021-01169-1
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Index Terms

A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

Journal of the ACM Volume 22, Issue 4

Oct. 1975

172 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321906

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1975

Published in JACM Volume 22, Issue 4

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Aihie IOkuonghae R(2024)A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEsEarthline Journal of Mathematical Sciences10.34198/ejms.14324.565588(565-588)Online publication date: 4-Apr-2024
https://doi.org/10.34198/ejms.14324.565588
Noren H(2023)Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta MethodsGeometric Science of Information10.1007/978-3-031-38271-0_55(552-559)Online publication date: 30-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-38271-0_55
Olatunji PIkhile MOkuonghae R(2021)Nested Second Derivative Two-Step Runge–Kutta MethodsInternational Journal of Applied and Computational Mathematics10.1007/s40819-021-01169-17:6Online publication date: 22-Nov-2021
https://doi.org/10.1007/s40819-021-01169-1
Kulikov G(2020)Nested Implicit Runge–Kutta Pairs of Gauss and Lobatto Types with Local and Global Error Controls for Stiff Ordinary Differential EquationsComputational Mathematics and Mathematical Physics10.1134/S096554252007007660:7(1134-1154)Online publication date: 9-Aug-2020
https://doi.org/10.1134/S0965542520070076
Brugnano LIavernaro FTrigiante D(2012)A two-step, fourth-order method with energy preserving propertiesComputer Physics Communications10.1016/j.cpc.2012.04.002183:9(1860-1868)Online publication date: Sep-2012
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Cash JMazzia F(2011)Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two Point Boundary Value ProblemsRecent Advances in Computational and Applied Mathematics10.1007/978-90-481-9981-5_2(23-39)Online publication date: 2011
https://doi.org/10.1007/978-90-481-9981-5_2
Kulikov GShindin S(2009)Adaptive nested implicit Runge--Kutta formulas of Gauss typeApplied Numerical Mathematics10.1016/j.apnum.2008.03.01959:3-4(707-722)Online publication date: 1-Mar-2009
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Głowacz ZGłowacz A(2007)Simulation language for analysis of discrete-continuous electrical systems (SELS2)Proceedings of the 26th IASTED International Conference on Modelling, Identification, and Control10.5555/1710594.1710614(94-99)Online publication date: 31-Jan-2007
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Glowacz ZGlowacz W(2007)Mathematical Model of DC Motor for Analysis of Commutation Processes2007 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives10.1109/DEMPED.2007.4393084(138-141)Online publication date: Sep-2007
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Cash J(2005)A Variable Step Runge--Kutta--Nyström Integrator for Reversible Systems of Second Order Initial Value ProblemsSIAM Journal on Scientific Computing10.1137/S03060172726:3(963-978)Online publication date: 1-Jan-2005
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Implicit Runge-Kutta Methods for Lipschitz Continuous Ordinary Differential Equations

The efficiency of Singly-implicit Runge-Kutta methods for stiff differential equations

Strong stability of singly-diagonally-implicit Runge--Kutta methods

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