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

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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.
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 
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     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/}
}
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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

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