article

Free access

A Transformed implicit Runge-Kutta Method

Author:

J. C. ButcherAuthors Info & Claims

Journal of the ACM (JACM), Volume 26, Issue 4

Pages 731 - 738

https://doi.org/10.1145/322154.322163

Published: 01 October 1979 Publication History

PDF eReader

References

[1]

BURRAGE, K. A special famdy of Runge-Kutta methods for solving surf differential equations. BIT 18 (1978), 22-41

Google Scholar

[2]

BUTCHER, J C On the implementation of tmphc~t Runge-Kutta methods BIT 16 (1976), 237-240

Google Scholar

[3]

FRANK, R, AND UEBERHUBER, C W. Iterated defect correctton for the effictent soluuon of staff systems of ordinary dlfferenUal equations BIT 17 (1977), 146-159

Google Scholar

[4]

NORSETT, S P Seml-exphclt Runge-Kutta methods Rep 6/74, Dept of Math, U ofTrondhe~m, Trondhe~m, Norway, 1974

Google Scholar

[5]

WOLFBRANDT, A A study of Rosenbrock processes with respect to order condmons and sttff stabd~ty Rep 77 01, Dept Comptr Sci, Chalmers Inst. of Technology, Goteborg, Sweden, 1977

Google Scholar

Cited By

View all

Butcher J(2016)ReferencesNumerical Methods for Ordinary Differential Equations10.1002/9781119121534.refs(499-507)Online publication date: Aug-2016
https://doi.org/10.1002/9781119121534.refs
Brugnano LIavernaro FMagherini C(2015)Efficient implementation of Radau collocation methodsApplied Numerical Mathematics10.1016/j.apnum.2014.09.00387(100-113)Online publication date: Jan-2015
https://doi.org/10.1016/j.apnum.2014.09.003
Brugnano LFrasca Caccia GIavernaro F(2014)Efficient implementation of Gauss collocation and Hamiltonian boundary value methodsNumerical Algorithms10.1007/s11075-014-9825-065:3(633-650)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1007/s11075-014-9825-0
Show More Cited By

Index Terms

A Transformed implicit Runge-Kutta Method
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Nonlinear equations

Recommendations

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

This paper deals with the numerical solution of initial value problems, for systems of ordinary differential equations, by Runge-Kutta methods (RKMs) with special nonlinear stability properties indicated by the terms total-variation-diminishing (TVD), ...
Implicit and Implicit---Explicit Strong Stability Preserving Runge---Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong ...
A new diagonally implicit Runge-Kutta-Nyström method for periodic IVPs

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Journal of the ACM Volume 26, Issue 4

Oct. 1979

231 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/322154

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1979

Published in JACM Volume 26, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

45
Total Citations
View Citations
912
Total Downloads

Downloads (Last 12 months)77
Downloads (Last 6 weeks)13

Reflects downloads up to 23 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Butcher J(2016)ReferencesNumerical Methods for Ordinary Differential Equations10.1002/9781119121534.refs(499-507)Online publication date: Aug-2016
https://doi.org/10.1002/9781119121534.refs
Brugnano LIavernaro FMagherini C(2015)Efficient implementation of Radau collocation methodsApplied Numerical Mathematics10.1016/j.apnum.2014.09.00387(100-113)Online publication date: Jan-2015
https://doi.org/10.1016/j.apnum.2014.09.003
Brugnano LFrasca Caccia GIavernaro F(2014)Efficient implementation of Gauss collocation and Hamiltonian boundary value methodsNumerical Algorithms10.1007/s11075-014-9825-065:3(633-650)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1007/s11075-014-9825-0
Butcher JImran G(2014)Symplectic effective order methodsNumerical Algorithms10.1007/s11075-013-9789-565:3(499-517)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1007/s11075-013-9789-5
Dambrosio RPaternoster B(2012)Two-step modified collocation methods with structured coefficient matricesApplied Numerical Mathematics10.1016/j.apnum.2012.06.00862:10(1325-1334)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1016/j.apnum.2012.06.008
Conte DD'Ambrosio RJackiewicz Z(2010)Two-step Runge-Kutta Methods with Quadratic Stability FunctionsJournal of Scientific Computing10.1007/s10915-010-9378-x44:2(191-218)Online publication date: 1-Aug-2010
https://dl.acm.org/doi/10.1007/s10915-010-9378-x
Jackiewicz Z(2009)ReferencesGeneral Linear Methods for Ordinary Differential Equations10.1002/9780470522165.refs(461-476)Online publication date: 10-Aug-2009
https://doi.org/10.1002/9780470522165.refs
Butcher JWright W(2006)Applications of doubly companion matricesApplied Numerical Mathematics10.5555/1642738.164290956:3-4(358-373)Online publication date: 1-Mar-2006
https://dl.acm.org/doi/10.5555/1642738.1642909
Butcher JWright W(2006)Applications of doubly companion matricesApplied Numerical Mathematics10.1016/j.apnum.2005.04.01456:3-4(358-373)Online publication date: Mar-2006
https://doi.org/10.1016/j.apnum.2005.04.014
Nørsett SSimonsen H(2006)Aspects of parallel Runge-Kutta methodsNumerical Methods for Ordinary Differential Equations10.1007/BFb0089234(103-117)Online publication date: 4-Oct-2006
https://doi.org/10.1007/BFb0089234
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

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

Implicit and Implicit---Explicit Strong Stability Preserving Runge---Kutta Methods with High Linear Order

A new diagonally implicit Runge-Kutta-Nyström method for periodic IVPs

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations