Sufficient conditions for the convergence of the Magnus expansion

Journal of Physics A: Mathematical and Theoretical

Volumn 40, Issue 50, 2007, Pages 15001-15017

  Casas, Fernando ^a  

^a UNIVERSITAT JAUME I   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36749044406     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/50/006     Document Type: Article

References (32)

1. Abramowitz M and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)
2. Blanes S, Casas F, Oteo J A and Ros J 1998 Magnus and Fer expansions for matrix differential equations: the convergence problem J. Phys. A: Math. Gen. 22 259-68
3. Blanes S, Casas F, Oteo J A and Ros J 2007 Magnus expansion: mathematical study and physical applications, work in progress
4. Blanes S, Casas F and Ros J 2000 Improved high order integrators based on the Magnus expansion BIT 40 434-50
5. Blanes S, Casas F and Ros J 2002 High order optimized geometric integrators for linear differential equations BIT 42 262-84
6. Chacon R V and Fomenko A T 1991 Recursion formulas for the Lie integral Adv. Math. 88 200-57
7. Coddington E A and Levinson N 1955 Theory of Ordinary Differential Equations (New York: McGraw-Hill)
8. Dixmier J 1957 L'application exponentielle dans les groupes de Lie résolubles Bull. Soc. Math. France 85 113-21
9. Dunford N and Schwartz J T 1958 Linear Operators. Part I: General Theory (New York: Wiley-Interscience)
10. Fel'dman E B 1984 On the convergence of the Magnus expansion for spin systems in periodic magnetic fields Phys. Lett. A 104 479-81
11. Gantmacher F R 1959 The Theory of Matrices (New York: Chelsea)
12. Gronwall T H 1919 Note on the derivatives with respect to a parameter of the solutions of a system of differential equation Ann. Math. 20 292-6
13. Hairer E, Lubich Ch and Wanner G 2006 Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations 2nd edn (Berlin: Springer)
14. Hunter J K and Nachtergaele B 2001 Applied Analysis (Singapore: World Scientific)
15. Iserles A, Munthe-Kaas H Z, Nørsett S P and Zanna A 2000 Lie-group methods Acta Numer. 9 215-365
16. 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
17. Karasev M V and Mosolova M V 1977 Infinite products and T products of exponentials J. Theor. Math. Phys. 28 721-30
18. Klarsfeld S and Oteo J A 1989 Analytic properties of the Magnus operator for two solvable Hamiltonians Phys. Lett. A 142 393-7
19. Klarsfeld S and Oteo J A 1989 Recursive generation of higher-order terms in the Magnus expansion Phys. Rev. A 39 3270-3273
20. Kurosh A G 1972 Higher Algebra (Paris: Mir)
21. Magnus W 1954 On the exponential solution of differential equations for a linear operator Commun. Pure Appl. Math. VII 649-73
22. Maricq M M 1987 Convergence of Magnus expansion for time-dependent two-level systems J. Chem. Phys. 86 5647-51
23. Mityagin B S 1990 Unpublished notes
24. Moan P C 1998 Efficient approximation of Sturm-Liouville problems using Lie-group methods Technical Report 1998/NA11 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
25. Moan P C, Oteo J A and Ros J 1999 On the existence of the exponential solution of linear differential systems J. Phys. A: Math. Gen. 32 5133-9
26. Moan P C 2002 On backward error analysis and Nekhoroshev stability in the numerical analysis of conservative systems of ODEs PhD Thesis University of Cambridge
27. Moan P C and Niesen J 2006 Convergence of the Magnus series Technical Report La Trobe University
28. Pechukas P and Light J C 1966 On the exponential form of time-displacement operators in quantum mechanics J. Chem. Phys. 44 3897-912
29. Saito M 1957 Sur certain groupes de Lie résolubles: I, II Sci. Pap. College Gen. Educ. Univ. Tokyo 7 1-11
30. Salzman W R 1986 Convergence of Magnus and Magnus-like expansions in the Schrödinger representation J. Chem. Phys. 85 4605-13
31. Wei J 1963 Note on global validity of the Baker-Hausdorff and Magnus theorems J. Math. Phys. 4 1337-41
32. Yakubovich V A and Starzhinskii V M 1975 Linear Differential Equations with Periodic Coefficients (New York: Wiley)