The adaptive Verlet method

SIAM Journal on Scientific Computing

Volumn 18, Issue 1, 1997, Pages 239-256

  Huang, Weizhang ^a   Leimkuhler, Benedict ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

Hamiltonian systems; Leapfrog; N body problems; Symplectic methods; Time reversible methods; Variable step size methods; Verlet

Indexed keywords

ADAPTIVE VERLET METHOD; HAMILTONIAN SYSTEMS; LEAPFROG METHOD; N BODY PROBLEMS; TIME REVERSIBLE METHODS; VARIABLE STEPSIZE METHODS;

INTEGRATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING; VECTORS;

VARIATIONAL TECHNIQUES;

EID: 0030621834     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595284658     Document Type: Article

References (22)

1. S. J. AARSETH, Integration methods for small N-body systems, in Predictability, Stability and Chaos in N-Body Dynamical Systems, A. E. Roy, ed., NATO ASI Series, Series B: Physics, North-Holland, Amsterdam, 1991.
2. K. BRENAN, S. CAMPBELL, AND L. R. PETZOLD, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
3. M. P. CALVO AND E. HAIRER, Accurate long-term integration of dynamical systems, Appl. Numer. Math., 18 (1995), pp. 95-105.
4. M. P. CALVO AND J. M. SANZ-SERNA, The development of variable-step symplectic integrators, with application to the two-body problem, SIAM J. Sci. Comput., 14 (1993), pp. 936-952.
5. G. J. COOPER, Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal., 7 (1987), pp. 1-13.
6. R. D. RUTH, A canonical integration technique, IEEE Trans. Nuc. Sci., 30 (1983), pp. 2669-2671.
7. C. W. GEAR AND R. D. SKEEL, Does variable stepsize ruin a symplectic integrator?, Physica D, 60 (1992), pp. 311-313.
8. G. SUN, Symplectic partitioned Runge-Kutta methods, J. Comput. Math., 11 (1993), pp. 365-372.
9. G. GOLUB AND C. VAN LOAN, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.
10. E. HAIRER, Backward error analysis of numerical integrators and symplectic methods, Ann. Numer. Math., 1 (1994), pp. 107-132.
11. P. HUT, J. MAKINO, AND S. MCMILLAN, Building a better leapfrog, Astrophysical Journal, 443 (1995), pp. L93-L96.
12. B. LEIMKUHLER, S. REICH, AND R. SKEEL, Numerical Integration Methods in Molecular Dynamics, 1994 IMA Summer Program: Moleculer Biology, K. Schulten and J. Mesirov, eds., Springer, to appear.
13. S. MIKKOLA AND K. INNANEN, A numerical experimenter's view of the few-body problem, in Predictability, Stability and Chaos in N-Body Dynamical Systems, A. E. Roy, ed., NATO ASI Series, Series B: Physics, North-Holland, Amsterdam, 1991.
14. D. OKUNBOR AND R. SKEEL, Explicit canonical methods for Hamiltonian systems, Math. Comp., 59 (1992), pp. 521-527.
15. K. RICHTER, G. TANNER, AND D. WINTGEN, Classical mechanics of two-electron atoms, Phys. Rev. A, 48 (1993), pp. 4182-4196.
16. J. M. SANZ-SERNA, Runge-Kutta schemes for Hamiltonian systems, BIT, 28 (1988), pp. 877-883.
17. J. M. SANZ-SERNA AND M. P. CALVO, Numerical Hamiltonian Problems, Chapman and Hall, London, 1994.
18. Y. SHIBBERU, Time-discretization of Hamiltonian dynamical systems, Comput. and Math. Appl., 28 (1994), pp. 123-146.
19. J, C. SIMO AND O. GONZALEZ, On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry, Comput. Methods Appl. Mech. Engrg., to appear.
20. R. D. SKEEL AND J. J. BIESIADECKI, Symplectic integration with variable stepsize, Ann. Numer. Math., 1 (1994), pp. 191-198.
21. D. M. STOFFER, Variable steps for reversible integration methods, Computing, 55 (1995), pp. 1-22.
22. J. WISDOM, Some aspects of chaotic behavior in the solar system, in The Few Body Problem, Proc. 96th Colloquium of the International Astronomical Union, M. J. Valtonen, ed., Turku, Finland, 1987.