Discrete gradient algorithms of high order for one-dimensional systems |
| |
| Authors: | Jan L. Cieśliński Bogusław Ratkiewicz |
| |
| Affiliation: | 1. Uniwersytet w Bia?ymstoku, Wydzia? Fizyki, ul. Lipowa 41, 15-424 Bia?ystok, Poland;2. I LO, ul. ?ródmie?cie 31, 16-300 Augustów, Poland;1. Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, Campus Universitario s/n, Ciudad Real C.P. 13005, Spain;2. Department of Automatica and Computer Science, Havana Polytechnic University, Calle 114 No 11901, CUJAE, Marianao, Habana C.P. 19390, Cuba |
| |
| Abstract: | We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories in the phase space. The accuracy of our integrators is higher by several orders of magnitude as compared with the standard discrete gradient scheme (modified midpoint rule) and, what is more, our schemes have very high accuracy even for large time steps. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
