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A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed.
A. Nordsieck: On numerical integration of ordinary differential equations, Math. Comput. 16 (1962), 22-49
1962
Earlier work this paper cites.
M.R. Osborne: On NORDSIECK’s method for the numerical solution of ordinary differential equations, BIT 6, (1966), 51-57
1966
Earlier work this paper cites.
A. Askar and S. Cakmak, J. Chem. Phys. 68, 2794 (1978)
1978
Earlier work this paper cites.
H. Tal-Ezer and R. Kosloff: An accurate and efficient scheme for propagating the time dependent Schrödinger equation, J. Chem. Phys. 81 (9) 3967-3971 (1984)
1984
Earlier work this paper cites.
M. Tuckerman, B.J. Berne, G.J. Martyna: Reversible multiple time scale dynamics, J. Chem. Phys. Vol. 97(3) pp. 1990 - 2001, 1992, Equation (2.22)
1992
Earlier work this paper cites.
William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery: Numerical Recipes in C, The Art of Scientific Computing, Second Edition, Cambridge University Press 1992
1992
Earlier work this paper cites.
J.M. Sanz-Serna and M.P. Calvo: Numerical Hamiltonian Problems, Applied Mathematics and Mathematical Computation 7, Chapman & Hall 1994
1994
Earlier work this paper cites.
A.M. Stuart and A.R. Humphries: Dynamical Systems and Numerical Analysis, Cambridge University Press, 1996
1996
Earlier work this paper cites.
T. Holder, B. Leimkuhler, and S. Reich: Explicit, time-reversible and variable step size integration. Appl. Numer. Math., 39:367-377,2001. http://opus.kobv.de/zib/volltexte/1998/361/pdf/SC-98-17.pdf
1998
Cited alongside, same era.
Ulrich Mutze: Predicting Classical Motion Directly from the Action Principle II Mathematical Physics Preprint Archive 1999–271 www.ma.utexas.edu/mp_arc/c/99/99-271.pdf
1999
Cited alongside, same era.
Ulrich Mutze: A Simple Variational Integrator for General Holonomic Mechanical Systems, Mathematical Physics Preprint Archive 2003–491 www.ma.utexas.edu/mp_arc/c/03/03-491.pdf
2003
Cited alongside, same era.
Ernst Hairer, Christian Lubich, Gerhard Wanner: Geometric numerical integration illustrated by the Størmer/Verlet method, Acta Numerica (2003) pp. 1-51 Cambridge University Press, 2003
2003
Cited alongside, same era.
Ulrich Mutze: The direct midpoint method as a quantum mechanical integrator II, Mathematical Physics Preprint Archive 2007–176 www.ma.utexas.edu/mp_arc/c/07/07-176.pdf
2007
Later among the works it cites.
Ulrich Mutze: An asynchronous leapfrog method (2008) Mathematical Physics Preprint Archive 2008–197 http://www.ma.utexas.edu/mp_arc/c/08/08-197.pdf
2008
Later among the works it cites.
Ulrich Mutze: Separated quantum dynamics Mathematical Physics Preprint Archive 2008–69 www.ma.utexas.edu/mp_arc/c/08/08-69.pdf
2008
Later among the works it cites.
Leaking Bucket Equation and Reversibility from The Wolfram Demonstrations Project. http://demonstrations.wolfram.com/LeakingBucketEquationAndReversibility/
2010
Later among the works it cites.
On the Stability Limit of Leapfrog Methods from The Wolfram Demonstrations Project. http://demonstrations.wolfram.com/OnTheStabilityLimitOfLeapfrogMethods/
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Benedict Leimkuhler and Sebastian Reich: Simulating Hamiltonian Dynamics, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press 2004
2004
Cited alongside, same era.
G. Gallavotti: Classical Mechanics http://ipparco.roma1.infn.it/pagine/deposito/2005/MC.ps.gz
2005
Cited alongside, same era.
Ulrich Mutze: The direct midpoint method as a quantum mechanical integrator, Mathematical Physics Preprint Archive 2006–356 www.ma.utexas.edu/mp_arc/c/06/06-356.pdf (2006)
2006
Cited alongside, same era.
Zdzislaw Jackiewicz (2007), General linear methods Scholarpedia, 2(4):2852. http://www.scholarpedia.org/article/General_linear_methods
2007
Cited alongside, same era.
Ulrich Mutze: homepage http://www.ulrichmutze.de/articles/leapfrog4.pdf
Cited in the paper.
Ulrich Mutze: Post at researchgate.net https://www.researchgate.net/post/Who_knows_of_an_integrator_for_the_general_first_order_ODE_which_is_second_order_and_needs_only_one_evaluation_of_the_equations_rhs_per_time_step
Cited in the paper.
Ulrich Mutze: homepage http://www.ulrichmutze.de/interactionpicturemovie1/intact1.html http://www.ulrichmutze.de/interactionpicturemovie2/intact2.html
Cited in the paper.
Ulrich Mutze: homepage http://www.ulrichmutze.de/softwaredescriptions/tut.pdf
Cited in the paper.
2011
Later among the works it cites.
Relativistic Quantum Dynamics in 1D and the Klein Paradox from The Wolfram Demonstrations Project. http://demonstrations.wolfram.com/RelativisticQuantumDynamicsIn1DAndTheKleinParadox/
2011
Later among the works it cites.
Goldstein, Safko, Poole: Classical Mechanics, Third Edition, Pearson Education Limited 2014
2014
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The Asynchronous Leapfrog Method as a Stiff ODE Solver from The Wolfram Demonstrations Project. http://demonstrations.wolfram.com/TheAsynchronousLeapfrogMethodAsAStiffODESolver/
2016
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