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Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations

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J. R. CashAuthors Info & Claims

Journal of the ACM (JACM), Volume 23, Issue 3

Pages 455 - 460

https://doi.org/10.1145/321958.321966

Published: 01 July 1976 Publication History

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Abstract

A -stable, semi-implicit Runge-Kutta procedures requiring at most one Jacobian evaluation per time step are developed for the approximate numerical integration of stiff systems of ordinary differential equations. A simple procedure for estimating the local truncation error is described and, with the help of this estimate, efficient integration procedures are derived. The algorithms are illustrated by direct application to a particular example.

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Hidayat YPurwandari TSubiyanto Sukono (2021)Identifying Unwanted Conditions through Chaotic Area Determination in the Context of Indonesia’s Economic Resilience at the City LevelSustainability10.3390/su1309518313:9(5183)Online publication date: 6-May-2021
https://doi.org/10.3390/su13095183
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
Liniger W(2006)Recent developments in stability and error analysis of numerical methods for ordinary differential equationsEquadiff 8210.1007/BFb0103268(420-431)Online publication date: 30-Dec-2006
https://doi.org/10.1007/BFb0103268
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Index Terms

Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
      1. Interpolation

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Published In

Journal of the ACM Volume 23, Issue 3

July 1976

175 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321958

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1976

Published in JACM Volume 23, Issue 3

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Hidayat YPurwandari TSubiyanto Sukono (2021)Identifying Unwanted Conditions through Chaotic Area Determination in the Context of Indonesia’s Economic Resilience at the City LevelSustainability10.3390/su1309518313:9(5183)Online publication date: 6-May-2021
https://doi.org/10.3390/su13095183
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
Liniger W(2006)Recent developments in stability and error analysis of numerical methods for ordinary differential equationsEquadiff 8210.1007/BFb0103268(420-431)Online publication date: 30-Dec-2006
https://doi.org/10.1007/BFb0103268
Burka M(2004)Solution of stiff ordinary differential equations by decomposition and orthogonal collocationAIChE Journal10.1002/aic.69028010428:1(11-20)Online publication date: 17-Jun-2004
https://doi.org/10.1002/aic.690280104
García-López C(2003)Piecewise-linearized and linearized θ-methods for ordinary and partial differential equationsComputers & Mathematics with Applications10.1016/S0898-1221(03)80023-845:1-3(351-381)Online publication date: Jan-2003
https://doi.org/10.1016/S0898-1221(03)80023-8
Colalongo LRudan M(1993)ROW-type Methods Applied To The Time Discretization Of Device Equations[Proceedings] 1993 International Workshop on VLSI Process and Device Modeling (1993 VPAD)10.1109/VPAD.1993.724751(124-125)Online publication date: 1993
https://doi.org/10.1109/VPAD.1993.724751
van der Houwen PSommeijer BCouzy W(1992)Embedded diagonally implicit Runge-Kutta algorithms on parallel computersMathematics of Computation10.1090/S0025-5718-1992-1106986-858:197(135-159)Online publication date: 1992
https://doi.org/10.1090/S0025-5718-1992-1106986-8
Kværnø A(1990)Runge-Kutta methods applied to fully implicit differential-algebraic equations of index 1Mathematics of Computation10.1090/S0025-5718-1990-1010600-854:190(583-625)Online publication date: 1990
https://doi.org/10.1090/S0025-5718-1990-1010600-8
Urbani A(1990)Metodi row modificati per problemi stiffCalcolo10.1007/BF0257615027:1-2(89-102)Online publication date: Mar-1990
https://doi.org/10.1007/BF02576150
(1988)REFERENCESNumerical Methods for Initial Value Problems in Ordinary Differential Equations10.1016/B978-0-12-249930-2.50016-3(247-286)Online publication date: 1988
https://doi.org/10.1016/B978-0-12-249930-2.50016-3
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The efficiency of Singly-implicit Runge-Kutta methods for stiff differential equations

Solving linear ordinary differential equations using singly diagonally implicit Runge-Kutta fifth order five-stage method

Implicit Runge-Kutta Methods for Lipschitz Continuous Ordinary Differential Equations

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