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Pseudo-Runge-Kutta Methods of the Fifth Order

Author:

William B. GruttkeAuthors Info & Claims

Journal of the ACM (JACM), Volume 17, Issue 4

Pages 613 - 628

https://doi.org/10.1145/321607.321611

Published: 01 October 1970 Publication History

Abstract

A family of fifth-order pseudo-Runge-Kutta methods for the numerical solution of systems of ordinary differential equations is presented. A procedure for determining an “optimal” set of parameters is given, and several examples are considered. The principal advantage of these methods is that, for a fixed stepsize, they require two less function evaluations at each step than do the corresponding fifth-order Runge-Kutta methods. Their principal disadvantage is that they are not self-starting; they require two initial values. Numerically, pseudo-Runge-Kutta and Runge-Kutta methods seem to be comparable.

References

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AND LAMBERT, R .J . Pseudo-Runge-Kutta methods involving two points. J. ACM 1 (1966), 114-123.

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HILDEBRAND, F .B . Introduction to Numerical Analysis. McGraw-Hill, New York, 1956.

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Cited By

Udwadia FFarahani A(2008)Accelerated Runge‐Kutta MethodsDiscrete Dynamics in Nature and Society10.1155/2008/7906192008:1Online publication date: 16-Sep-2008
https://doi.org/10.1155/2008/790619
Stickler MPanke DHamielec A(2003)Polymerization of methyl methacrylate up to high degrees of conversion: Experimental investigation of the diffusion‐controlled polymerizationJournal of Polymer Science: Polymer Chemistry Edition10.1002/pol.1984.17022092422:9(2243-2253)Online publication date: 11-Mar-2003
https://doi.org/10.1002/pol.1984.170220924
Stickler M(2003)Free‐radical polymerization kinetics of methyl methacrylate at very high conversionsDie Makromolekulare Chemie10.1002/macp.1983.021841216184:12(2563-2579)Online publication date: 12-Mar-2003
https://doi.org/10.1002/macp.1983.021841216
Show More Cited By

Index Terms

Pseudo-Runge-Kutta Methods of the Fifth Order
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 17, Issue 4

Oct. 1970

169 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321607

Issue’s Table of Contents

Copyright © 1970 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1970

Published in JACM Volume 17, Issue 4

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Cited By

Udwadia FFarahani A(2008)Accelerated Runge‐Kutta MethodsDiscrete Dynamics in Nature and Society10.1155/2008/7906192008:1Online publication date: 16-Sep-2008
https://doi.org/10.1155/2008/790619
Stickler MPanke DHamielec A(2003)Polymerization of methyl methacrylate up to high degrees of conversion: Experimental investigation of the diffusion‐controlled polymerizationJournal of Polymer Science: Polymer Chemistry Edition10.1002/pol.1984.17022092422:9(2243-2253)Online publication date: 11-Mar-2003
https://doi.org/10.1002/pol.1984.170220924
Stickler M(2003)Free‐radical polymerization kinetics of methyl methacrylate at very high conversionsDie Makromolekulare Chemie10.1002/macp.1983.021841216184:12(2563-2579)Online publication date: 12-Mar-2003
https://doi.org/10.1002/macp.1983.021841216
Panke DStickler MWunderlich W(2003)Zur polymerisation von methylmethacrylat bis zu hohen umsätzen: Experimentelle untersuchungen zur theorie des trommsdorff‐effektes nach cardenas und o'driscollDie Makromolekulare Chemie10.1002/macp.1983.021840118184:1(175-191)Online publication date: 12-Mar-2003
https://doi.org/10.1002/macp.1983.021840118
Bader M(1987)A comparative study of new truncation error estimates and intrinsic accuracies of some higher order Runge-Kutta algorithmsComputers & Chemistry10.1016/0097-8485(87)80030-X11:2(121-124)Online publication date: Jan-1987
https://doi.org/10.1016/0097-8485(87)80030-X
Shintani H(1981)On pseudo-Runge-Kutta methods of the third kindHiroshima Mathematical Journal10.32917/hmj/120613409911:2Online publication date: 1-Jan-1981
https://doi.org/10.32917/hmj/1206134099
Shintani H(1971)On one-step methods utilizing the second derivativeHiroshima Mathematical Journal10.32917/hmj/12061379791:2Online publication date: 1-Jan-1971
https://doi.org/10.32917/hmj/1206137979

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