Splitting methods for non-autonomous separable dynamical systems

Journal of Physics A: Mathematical and General

Volumn 39, Issue 19, 2006, Pages 5405-5423

  Blanes, S ^a   Casas, F ^b  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

^b UNIVERSITAT JAUME I   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646256122     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/19/S05     Document Type: Article

References (24)

1. Arnold V I 1989 Mathematical Methods of Classical Mechanics 2nd edn (New York: Springer)
2. Blanes S, Casas F and Ros J 2000 Improved high order integrators based on Magnus expansion BIT 40 434-50
3. Blanes S, Casas F and Ros J 2002 High order optimized geometric integrators for linear differential equations BIT 42 262-84
4. Blanes S and Moan P C 2000 Splitting methods for the time-dependent Schrödinger equation Phys. Lett. A 265 35-42
5. Blanes S and Moan P C 2001 Splitting methods for non-autonomous Hamiltonian equations J. Comput. Phys. 170 205-30
6. Blanes S and Moan P C 2002 Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods J. Comput. Appl. Math. 142 313-30
7. Blanes S and Moan P C Fourth- and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems Appl. Num. Math. (at press)
8. Gray S and Manolopoulos D E 1996 Symplectic integrators tailored to the time-dependent Schrödinger equation J. Chem. Phys. 104 7099-112
9. Guckenheimer J and Holmes P 1983 Nonlinear Oscillators, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer)
10. Hairer E, Lubich C and Wanner G 2002 Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (Berlin: Springer)
11. Iserles A, Munthe-Kaas H Z, Nørsett S P and Zanna A 2000 Lie group methods Acta Numer. 9 215-365
12. Iserles A and Nørsett S P 1999 On the solution of linear differential equations in Lie groups Phil. Trans. R. Soc. A 357 983-1019
13. Leimkuhler B and Reich S 2004 Simulating Hamiltonian Dynamics (Cambridge: Cambridge University Press)
14. Magnus W 1954 On the exponential solution of differential equations for a linear operator Commun. Pure Appl. Math. 7 649-73
15. McLachlan R I 1995 On the numerical integration of ordinary differential equations by symmetric composition methods SIAM J. Sci. Comput. 16 151-68
16. McLachlan R I 1995 Composition methods in the presence of small parameters BIT 35 258-68
17. McLachlan R I and Quispel R 2002 Splitting methods Acta Numer. 11 341-434
18. Munthe-Kaas H and Owren B 1999 Computations in a free Lie algebra Phil. Trans. R. Soc. A 357 957-81
19. Paul Raj S, Rajasekar S and Murali K 1999 Coexisting chaotic attractors, their basin of attraction and synchronization of chaos in two coupled Duffing oscillators Phys. Lett. A 264 283-8
20. Sanz-Serna J M and Calvo M P 1994 Numerical Hamiltonian Problems (London: Chapman & Hall)
21. Sanz-Serna J M and Portillo A 1966 Classical numerical integrators for wave-packet dynamics J. Chem. Phys. 104 2349-55
22. Suzuki M 1990 Fractal decomposition of exponential operators with applications to many-body theories and Monte C arlo simulations Phys. Lett. A 146 319-23
23. Varadarajan V S 1984 Lie Groups, Lie Algebras, and Their Representations (New York: Springer)
24. Yoshida H 1990 Construction of higher order symplectic integrators Phys. Lett. A 150 262-8