Geodesic
A modified version of explicit Runge-Kutta methods for energy-preserving
Kybernetika, Tome 50 (2014) no. 5, pp. 838-847
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.14736/kyb-2014-5-0838
Classification : 34A34, 65L05, 65L06, 65L07
Keywords: energy-preserving; explicit Runge–Kutta methods; gradient 
@article{10_14736_kyb_2014_5_0838,
     author = {Hu, Guang-Da},
     title = {A modified version of explicit {Runge-Kutta} methods for energy-preserving},
     journal = {Kybernetika},
     pages = {838--847},
     year = {2014},
     volume = {50},
     number = {5},
     doi = {10.14736/kyb-2014-5-0838},
     mrnumber = {3301864},
     zbl = {06410707},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-5-0838/}
}
TY  - JOUR
AU  - Hu, Guang-Da
TI  - A modified version of explicit Runge-Kutta methods for energy-preserving
JO  - Kybernetika
PY  - 2014
SP  - 838
EP  - 847
VL  - 50
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-5-0838/
DO  - 10.14736/kyb-2014-5-0838
LA  - en
ID  - 10_14736_kyb_2014_5_0838
ER  - 
%0 Journal Article
%A Hu, Guang-Da
%T A modified version of explicit Runge-Kutta methods for energy-preserving
%J Kybernetika
%D 2014
%P 838-847
%V 50
%N 5
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-5-0838/
%R 10.14736/kyb-2014-5-0838
%G en
%F 10_14736_kyb_2014_5_0838
Hu, Guang-Da. A modified version of explicit Runge-Kutta methods for energy-preserving. Kybernetika, Tome 50 (2014) no. 5, pp. 838-847. doi: 10.14736/kyb-2014-5-0838

[1] Brugnano, L., Calvo, M., Montijano, J. I., Rândez, L.: Energy-preserving methods for Poisson systems. J. Comput. Appl. Math. 236 (2012), 3890-3904. | DOI | MR | Zbl

[2] 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. | MR

[3] Calvo, M., Laburta, M. P., Montijano, J. I., Rândez, L.: Error growth in numerical integration of periodic orbits. Math. Comput. Simul. 81 (2011), 2646-2661. | DOI | MR

[4] Calvo, M., Iserles, A., Zanna, A.: Numerical solution of isospectral flows. Math. Comput. 66 (1997), 1461-1486. | DOI | MR | Zbl

[5] Cooper, G. J.: Stability of Runge-Kutta methods for trajectory problems. IMA J. Numer. Anal. 7 (1987), 1-13. | DOI | MR | Zbl

[6] Buono, N. Del, Mastroserio, C.: Explicit methods based on a class of four stage Runge-Kutta methods for preserving quadratic laws. J. Comput. Appl. Math. 140 (2002), 231-243. | DOI | MR

[7] Griffiths, D. F., Higham, D. J.: Numerical Methods for Ordinary Differential Equations. Springer-Verlag, London 2010. | MR | Zbl

[8] Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Springer-Verlag, Berlin 2002. | MR | Zbl

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

[10] Lee, T., Leok, M., McClamroch, N. H.: Lie variational integrators for the full body problem in orbital methanics. Celest. Meth. Dyn. Astr. 98 (2007), 121-144. | DOI | MR

[11] Li, S.: Introduction to Classical Mechanics. (In Chinese.). University of Science and Technology of China, Hefei 2007.

[12] Shampine, L. F.: Conservation laws and numerical solution of ODEs. Comput. Math. Appl. 12B (1986), 1287-1296. | DOI | MR

Cité par Sources :