# A modified version of explicit Runge-Kutta methods for energy-preserving

Kybernetika (2014)

- Volume: 50, Issue: 5, page 838-847
- ISSN: 0023-5954

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topHu, Guang-Da. "A modified version of explicit Runge-Kutta methods for energy-preserving." Kybernetika 50.5 (2014): 838-847. <http://eudml.org/doc/262172>.

@article{Hu2014,

abstract = {In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.},

author = {Hu, Guang-Da},

journal = {Kybernetika},

keywords = {energy-preserving; explicit Runge–Kutta methods; gradient; energy-preserving; explicit Runge-Kutta methods; conservative system; numerical experiment},

language = {eng},

number = {5},

pages = {838-847},

publisher = {Institute of Information Theory and Automation AS CR},

title = {A modified version of explicit Runge-Kutta methods for energy-preserving},

url = {http://eudml.org/doc/262172},

volume = {50},

year = {2014},

}

TY - JOUR

AU - Hu, Guang-Da

TI - A modified version of explicit Runge-Kutta methods for energy-preserving

JO - Kybernetika

PY - 2014

PB - Institute of Information Theory and Automation AS CR

VL - 50

IS - 5

SP - 838

EP - 847

AB - In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.

LA - eng

KW - energy-preserving; explicit Runge–Kutta methods; gradient; energy-preserving; explicit Runge-Kutta methods; conservative system; numerical experiment

UR - http://eudml.org/doc/262172

ER -

## References

top- Brugnano, L., Calvo, M., Montijano, J. I., Rândez, L., 10.1016/j.cam.2012.02.033, J. Comput. Appl. Math. 236 (2012), 3890-3904. Zbl1247.65092MR2926249DOI10.1016/j.cam.2012.02.033
- Brugnano, L., Iavernaro, F., Trigiante, D., Hamiltonian boundary value methods (energy-preserving discrete line integral methods)., J. Numer. Anal. Ind. Appl. Math. 5 (2010), 1-2, 17-37. MR2833606
- Calvo, M., Laburta, M. P., Montijano, J. I., Rândez, L., 10.1016/j.matcom.2011.05.007, Math. Comput. Simul. 81 (2011), 2646-2661. MR2822275DOI10.1016/j.matcom.2011.05.007
- Calvo, M., Iserles, A., Zanna, A., 10.1090/S0025-5718-97-00902-2, Math. Comput. 66 (1997), 1461-1486. Zbl0907.65067MR1434938DOI10.1090/S0025-5718-97-00902-2
- Cooper, G. J., 10.1093/imanum/7.1.1, IMA J. Numer. Anal. 7 (1987), 1-13. Zbl0624.65057MR0967831DOI10.1093/imanum/7.1.1
- Buono, N. Del, Mastroserio, C., 10.1016/S0377-0427(01)00398-3, J. Comput. Appl. Math. 140 (2002), 231-243. MR1934441DOI10.1016/S0377-0427(01)00398-3
- Griffiths, D. F., Higham, D. J., Numerical Methods for Ordinary Differential Equations., Springer-Verlag, London 2010. Zbl1209.65070MR2759806
- Hairer, E., Lubich, C., Wanner, G., Geometric Numerical Integration., Springer-Verlag, Berlin 2002. Zbl1228.65237MR1904823
- Khalil, H. K., Nonlinear Systems. Third Edition., Prentice Hall, Upper Saddle River, NJ 2002.
- Lee, T., Leok, M., McClamroch, N. H., 10.1007/s10569-007-9073-x, Celest. Meth. Dyn. Astr. 98 (2007), 121-144. MR2321987DOI10.1007/s10569-007-9073-x
- Li, S., Introduction to Classical Mechanics. (In Chinese.), University of Science and Technology of China, Hefei 2007.
- Shampine, L. F., 10.1016/0898-1221(86)90253-1, Comput. Math. Appl. 12B (1986), 1287-1296. MR0871366DOI10.1016/0898-1221(86)90253-1

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