article

Free access

Algorithm 670: a Runge-Kutta-Nyström code

Editor: John R. Rice Authors:

W. L. SewardAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 15, Issue 1

Pages 31 - 40

https://doi.org/10.1145/62038.69650

Published: 01 March 1989 Publication History

PDF eReader

Supplementary Material

GZ File (670.gz)

Runge-Kutta-Nystrom. Two embedded formula pairs are provided, the lower order pair allowing interpolation Gams: I1a1a

Download
39.05 KB

References

[1]

BRANKIN, R. W., DORMAND, J. R., GLADWELL, I., PRINCE, P. J., AND SEWARD, W. A Runge- Kutta-Nystr6m Code. Num. Anal. Rep. 136, University of Manchester, Manchester, England, 1987.

Google Scholar

[2]

DORMAND, J. R., AND PRINCE, P.J. New Runge-Kutta-Nystr6m algorithms for simulation in dynamical astronomy. Celestial Mechanics 18 (1978), 223-232.

Google Scholar

[3]

DORMAND, J. R., AND PRINCE, P.J. Runge-Kutta-Nystrbm triples. Comp. and Math. with Appl. 14 (1988), 1007-1017.

Google Scholar

[4]

DORMAND, J. R., EL-MIKKAWY, M. E. A., AND PRINCE, P.J. Families of Runge-Kutta-Nystr6m formulae. IMA J. Numer. Anal. 7 (1987), 235-250.

Google Scholar

[5]

DORMAND, J. R., EL-MIKKAWY, M. E. A., AND PRINCE, P.Z. High order embedded Runge- Kutta-NystrSm formulae. IMA J. Nurner. Anal. 7 (1987), 423-430.

Google Scholar

[6]

ENRIGHT, W. H., JACKSON, K. R., NORSETT, S. P., AND THOMSEN, P.G. Interpolants for Runge-Kutta formulas. ACM Trans. Math. Softw. I2, 3 (Sept. 1986), 193-218.

Crossref

Google Scholar

[7]

FEHLBERG, E. Classical eighth and lower order Runge-Kutta-Nystr6m formulas with step size control for special second order differential equations. NASA Tech. Rep. R-381, Washington, D.C., 1972.

Google Scholar

[8]

FILIPPI, S., AND GRhF, J. New Runge-Kutta-Nystr6m formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y" = f(x, y). J Comput. Appl. Math. 14 (1986), 361-370.

Crossref

Google Scholar

[9]

GLADWELL, I. Initial value routines in the NAG library. ACM Trans. Math. Softw. 5, 4 (Dec. 1979), 386-400.

Crossref

Google Scholar

[10]

GLADWELL, I., BERZlNS, M., AND BRANKIN, R.W. Design of stiff integrators in the NAG library. SIGNUM 23 (1988), 16-23.

Crossref

Google Scholar

[11]

GLADWELL, I., SHAMPINE, L. F., AND BRANKIN, R.W. Automatic selection of the initial step size for an ODE solver. J. Comput. Appl. Math. 18 (1987), 175-192.

Crossref

Google Scholar

[12]

GLADWELL, I., SHAMPINE, L. F., AND BRANKIN, R.W. Locating special events when solving ODEs. Appl. Math. Lett. 1 (1988), 153-156.

Google Scholar

[13]

GLADWELL, I., SHAMPINE, L. F., BACh, L. S., AND BRANKIN, R. W. Practical aspects of interpolation with Runge-Kutta codes. SIAM J. Sci. Stat. Comput. 8 (1987), 322-341.

Crossref

Google Scholar

[14]

HAIRER, E. M~thodes de Nystr6m pour l'~quation differentielle y" = f(x, y). Numer. Math. 27 (1977), 283-300.

Google Scholar

[15]

HORN, M.K. Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output. SIAM J. Numer. Anal. 20 (1983) 558-568.

Google Scholar

[16]

ISTPF, Toolpack/1 Release 2.1, PFORT-77 portability verifier. NAG Publication NP1312, Numerical Algorithms Group Ltd., Oxford, England.

Google Scholar

[17]

SHAMPINE, L.F.Storage reduction for Runge-Kutta codes. ACM Trans. Math. Softw. 5, 3 (Sept. 1979), 245-250.

Crossref

Google Scholar

[18]

SHAMPINE, L.F. Interpolation for Runge-Kutta methods. SIAM J. Numer. Anal. 22 (1985), 1014-1027.

Google Scholar

[19]

SHAMPINE, L.F. Some practical Runge-Kutta formulas. Math. Comput. 46 (1986), 135-150.

Crossref

Google Scholar

[20]

SHAMPINE, L. F., AND WATTS, H.A. The art of writing a Runge-Kutta code, Part I. Mathematical Software III, J. R. Rice, Ed. Academic Press, Orlando, Fla., 1977, 257-275.

Google Scholar

[21]

SHAMPINE, L. F., AND WATTS, H.A. The art of writing a Runge-Kutta code, II. Appl. Math. Comput. 5 (1979), 93-121.

Google Scholar

[22]

SHAMPINE, L. F., AND WATTS, H.A. DEPAC--Design of a user-oriented package of ODE solvers. Tech. Rep. SAND79-2374, Sandia National Laboratories, Albuquerque, N. Mex.

Google Scholar

[23]

VAST VERSION 1.22W. Pacific-Sierra Research, Mill Valley, Calif.

Google Scholar

Cited By

View all

Alharbi HYadav KRamadan RJerbi HSimos TTsitouras C(2024)Nine-Stage Runge–Kutta–Nyström Pairs Sharing Orders Eight and SixMathematics10.3390/math1202031612:2(316)Online publication date: 18-Jan-2024
https://doi.org/10.3390/math12020316
Kovalnogov VFedorov RKarpukhina MKornilova MSimos TTsitouras C(2024)Economical handling of Runge–Kutta–Nyström step rejectionJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115528438(115528)Online publication date: Mar-2024
https://doi.org/10.1016/j.cam.2023.115528
Porter SCanup R(2023)Orbits and Masses of the Small Satellites of PlutoThe Planetary Science Journal10.3847/PSJ/acde774:7(120)Online publication date: 11-Jul-2023
https://doi.org/10.3847/PSJ/acde77
Show More Cited By

Index Terms

Algorithm 670: a Runge-Kutta-Nyström code
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
  2. Mathematical software

Recommendations

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-...
Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients

In this paper, we consider Runge-Kutta-Nyström (RKN) methods applied to nonlinear Schrödinger equations with variable coefficients (NLSEvc). Concatenating symplectic Nyström methods in spatial direction and symplectic Runge-Kutta methods in temporal ...
Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations

Classical Runge-Kutta-Nyström (RKN) methods for second-order ordinary differential equations are extended to two-derivative Runge-Kutta-Nyström (TDRKN) methods involving the third derivative of the solution. A new version of Nyström tree theory and the ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 15, Issue 1

March 1989

89 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/62038

Editor:
John R. Rice

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 1989

Published in TOMS Volume 15, Issue 1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Badges

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

42
Total Citations
View Citations
2,467
Total Downloads

Downloads (Last 12 months)127
Downloads (Last 6 weeks)27

Reflects downloads up to 24 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Alharbi HYadav KRamadan RJerbi HSimos TTsitouras C(2024)Nine-Stage Runge–Kutta–Nyström Pairs Sharing Orders Eight and SixMathematics10.3390/math1202031612:2(316)Online publication date: 18-Jan-2024
https://doi.org/10.3390/math12020316
Kovalnogov VFedorov RKarpukhina MKornilova MSimos TTsitouras C(2024)Economical handling of Runge–Kutta–Nyström step rejectionJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115528438(115528)Online publication date: Mar-2024
https://doi.org/10.1016/j.cam.2023.115528
Porter SCanup R(2023)Orbits and Masses of the Small Satellites of PlutoThe Planetary Science Journal10.3847/PSJ/acde774:7(120)Online publication date: 11-Jul-2023
https://doi.org/10.3847/PSJ/acde77
Kovalnogov VMatveev AGeneralov DKarpukhina TSimos TTsitouras C(2023)Runge–Kutta–Nyström Pairs of Orders 8(6) for Use in Quadruple Precision ComputationsMathematics10.3390/math1104089111:4(891)Online publication date: 9-Feb-2023
https://doi.org/10.3390/math11040891
Kovalnogov VFedorov RKarpukhina MKornilova MSimos TTsitouras C(2023)Runge–Kutta–Nyström methods of eighth order for addressing Linear Inhomogeneous problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114778419(114778)Online publication date: Feb-2023
https://doi.org/10.1016/j.cam.2022.114778
Porter SSpencer JVerbiscer ABenecchi SWeaver HWen Lin HKavelaars JFraser WGerdes DBuie MSinger KParker JStern S(2022)Orbits and Occultation Opportunities of 15 TNOs Observed by New HorizonsThe Planetary Science Journal10.3847/PSJ/ac34913:1(23)Online publication date: 26-Jan-2022
https://doi.org/10.3847/PSJ/ac3491
Jerbi HOmri MKchaou MSimos TTsitouras C(2022)Runge-Kutta-Nyström Pairs of Orders 8(6) with Coefficients Trained to Perform Best on Classical OrbitsMathematics10.3390/math1004065410:4(654)Online publication date: 19-Feb-2022
https://doi.org/10.3390/math10040654
Chavez CGeorgakarakos NAviles AAceves HTovmassian GZharikov SPerez–Leon JTamayo F(2022)Testing the third-body hypothesis in the cataclysmic variables LU Camelopardalis, QZ Serpentis, V1007 Herculis and BK LyncisMonthly Notices of the Royal Astronomical Society10.1093/mnras/stac1112514:3(4629-4638)Online publication date: 5-Jul-2022
https://doi.org/10.1093/mnras/stac1112
Chavez CAviles AGeorgakarakos NRamos CAceves HTovmassian GZharikov S(2020)REVISITING FS AURIGAE AND ITS TRIPLE CATACLYSMIC VARIABLE SYSTEM HYPOTHESISRevista Mexicana de Astronomía y Astrofísica10.22201/ia.01851101p.2020.56.01.0456:1(19-28)Online publication date: 1-Apr-2020
https://doi.org/10.22201/ia.01851101p.2020.56.01.04
Mašín ZBenda JGorfinkiel JHarvey ATennyson J(2019)UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix methodComputer Physics Communications10.1016/j.cpc.2019.107092(107092)Online publication date: Dec-2019
https://doi.org/10.1016/j.cpc.2019.107092
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.

Supplementary Material

References

Cited By

Index Terms

Recommendations

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

Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients

Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Badges

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