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A Lie--Deprit perturbation algorithm for linear differential equations with periodic coefficients
1. | Institut de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, E-12071 Castellón, Spain |
2. | Institut de Matemàtiques i Aplicacions de Castelló (IMAC), and Departament de Matemàtiques, Universitat Jaume I, E-12071 Castellón, Spain |
References:
[1] |
L. Ya. Adrianova, "Introduction to Linear Systems of Differential Equations," American Mathematical Society, Providence, R.I., 1995. |
[2] |
S. Blanes, F. Casas, J. A. Oteo and J. Ros, The Magnus expansion and some of its applications, Phys. Rep., 470 (2009), 151-238.
doi: 10.1016/j.physrep.2008.11.001. |
[3] |
V. Burd, "Method of Averaging for Differential Equations on an Infinite Interval," Chapman & Hall / CRC, 2007.
doi: 10.1201/9781584888758. |
[4] |
F. Casas, J. A. Oteo and J. Ros, Floquet theory: Exponential perturbative treatment, J. Phys. A: Math. Gen., 34 (2001), 3379-3388.
doi: 10.1088/0305-4470/34/16/305. |
[5] |
F. Casas, J. A. Oteo and J. Ros, Unitary transformations depending on a small parameter, Proc. R. Soc. A, 468 (2012), 685-700.
doi: 10.1098/rspa.2011.0388. |
[6] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw-Hill, 1955. |
[7] |
A. Deprit, Canonical transformations depending on a small parameter, Celes. Mech., 1 (1969), 12-30.
doi: 10.1007/BF01230629. |
[8] |
M. G. Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Ann. École Norm. Sup., Ser. (2), 12 (1883), 47-89. |
[9] |
J. K. Hale, "Ordinary Differential Equations," Krieger Publishing, Florida, 1980. |
[10] |
A. Iserles and S. P. Nørsett, On the solution of linear differential equations in Lie groups, Phil. Trans. Royal Soc. A, 357 (1999), 983-1019.
doi: 10.1098/rsta.1999.0362. |
[11] |
A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), 215-365.
doi: 10.1017/S0962492900002154. |
[12] |
S. Klarsfeld and J. A. Oteo, Recursive generation of higher-order terms in the Magnus expansion, Phys. Rev. A, 39 (1989), 3270-3273.
doi: 10.1103/PhysRevA.39.3270. |
[13] |
E. S. Mananga and T. Charpentier, Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy, J. Chem. Phys., 135 (2011), 044109.
doi: 10.1063/1.3610943. |
[14] |
W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., 7 (1954), 649-673.
doi: 10.1002/cpa.3160070404. |
[15] |
F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, "NIST Handbook of Mathematical Functions," Cambridge University Press, 2010. |
[16] |
V. A. Yakubovich and V. M. Starzhinskii, "Linear Differential Equations with Periodic Coefficients," John Wiley & Sons, 1975. |
show all references
References:
[1] |
L. Ya. Adrianova, "Introduction to Linear Systems of Differential Equations," American Mathematical Society, Providence, R.I., 1995. |
[2] |
S. Blanes, F. Casas, J. A. Oteo and J. Ros, The Magnus expansion and some of its applications, Phys. Rep., 470 (2009), 151-238.
doi: 10.1016/j.physrep.2008.11.001. |
[3] |
V. Burd, "Method of Averaging for Differential Equations on an Infinite Interval," Chapman & Hall / CRC, 2007.
doi: 10.1201/9781584888758. |
[4] |
F. Casas, J. A. Oteo and J. Ros, Floquet theory: Exponential perturbative treatment, J. Phys. A: Math. Gen., 34 (2001), 3379-3388.
doi: 10.1088/0305-4470/34/16/305. |
[5] |
F. Casas, J. A. Oteo and J. Ros, Unitary transformations depending on a small parameter, Proc. R. Soc. A, 468 (2012), 685-700.
doi: 10.1098/rspa.2011.0388. |
[6] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw-Hill, 1955. |
[7] |
A. Deprit, Canonical transformations depending on a small parameter, Celes. Mech., 1 (1969), 12-30.
doi: 10.1007/BF01230629. |
[8] |
M. G. Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Ann. École Norm. Sup., Ser. (2), 12 (1883), 47-89. |
[9] |
J. K. Hale, "Ordinary Differential Equations," Krieger Publishing, Florida, 1980. |
[10] |
A. Iserles and S. P. Nørsett, On the solution of linear differential equations in Lie groups, Phil. Trans. Royal Soc. A, 357 (1999), 983-1019.
doi: 10.1098/rsta.1999.0362. |
[11] |
A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), 215-365.
doi: 10.1017/S0962492900002154. |
[12] |
S. Klarsfeld and J. A. Oteo, Recursive generation of higher-order terms in the Magnus expansion, Phys. Rev. A, 39 (1989), 3270-3273.
doi: 10.1103/PhysRevA.39.3270. |
[13] |
E. S. Mananga and T. Charpentier, Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy, J. Chem. Phys., 135 (2011), 044109.
doi: 10.1063/1.3610943. |
[14] |
W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., 7 (1954), 649-673.
doi: 10.1002/cpa.3160070404. |
[15] |
F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, "NIST Handbook of Mathematical Functions," Cambridge University Press, 2010. |
[16] |
V. A. Yakubovich and V. M. Starzhinskii, "Linear Differential Equations with Periodic Coefficients," John Wiley & Sons, 1975. |
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