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

Guang-Da Hu

Kybernetika (2014)

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

Abstract

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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.

How to cite

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Hu, 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

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  9. Khalil, H. K., Nonlinear Systems. Third Edition., Prentice Hall, Upper Saddle River, NJ 2002. 
  10. 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
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