Access the full text.
Sign up today, get DeepDyve free for 14 days.
G. Elenin, P. Shlyakhov (2011)
The geometric stricture of the parameter space of the three-stage symplectic Runge-Kutta methodsMathematical Models and Computer Simulations, 3
Yukitaka Minesaki, Yoshimasa Nakamura (2002)
A new discretization of the Kepler motion which conserves the Runge-Lenz vectorPhysics Letters A, 306
G. Elenin, T. Elenina (2015)
A one-parameter family of difference schemes for the numerical solution of the Keplerian problemComputational Mathematics and Mathematical Physics, 55
C. Brooks (1989)
Computer simulation of liquidsJournal of Solution Chemistry, 18
E. Hairer, S. Nørsett, G. Wanner (2009)
Solving Ordinary Differential Equations I: Nonstiff Problems
R. McLachlan, G. Quispel, N. Robidoux (1999)
Geometric integration using discrete gradientsPhilosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 357
Yu.B. Suris (1988)
Chislennoe reshenie obyknovennykh differentsial’nykh uravnenii
G.N. Duboshin (1963)
Nebesnaya mekhanika. Osnovnye zadachi i metody
L. Verlet (1967)
Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones MoleculesPhysical Review, 159
(1963)
Osnovnye zadachi i metody (Celestial Mechanics: Main Problems and Methods)
M. J. (2005)
RUNGE-KUTTA SCHEMES FOR HAMILTONIAN SYSTEMS
J. Marsden, Matthew West (2001)
Discrete mechanics and variational integratorsActa Numerica, 10
R. Scott, Michael Allen, D. Tildesley (1988)
Computer Simulation of Liquids
E. Faou, E. Hairer, M. Hochbruck, C. Lubich (2006)
Geometric Numerical Integration
R. Kozlov (2007)
Conservative discretizations of the Kepler motionJournal of Physics A: Mathematical and Theoretical, 40
(1979)
Matematicheskie metody klassicheskoi mekhaniki
(1987)
Translated under the title Reshenie obyknovennykh differentsial'nykh uravnenii. I. Nezhestkie zadachi
(1988)
On the conservation of the symplectic structure in numerical solutions of Hamiltonian systems
S. Reich (1994)
Momentum conserving symplectic integratorsPhysica D: Nonlinear Phenomena, 76
J. Cieśliński (2006)
An orbit-preserving discretization of the classical Kepler problemPhysics Letters A, 370
S. Linge, H. Langtangen (2019)
Solving Ordinary Differential EquationsProgramming for Computations - Python
(1997)
Symplectic Runge–Kutta schemes II: classification of symmetric methods
R. LaBudde, D. Greenspan (1974)
Discrete mechanics—A general treatmentJournal of Computational Physics, 15
L. Einkemmer (2016)
Structure preserving numerical methods for the Vlasov equationarXiv: Numerical Analysis
L.D. Landau, E.M. Lifshits (1973)
Mekhanika
We suggest and substantiate a unified form of a family of adaptive conservative numerical methods for the Kepler problem. The family contains methods of the second, fourth, and sixth approximation order as well as an exact method. The methods preserve all the global properties of the exact solution of the problem. The variable time step is chosen automatically depending on the properties of the solution.
Differential Equations – Springer Journals
Published: Aug 23, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.