F. [. Blanes and . Casas, On the necessity of negative coefficients for operator splitting schemes of order higher than two, Applied Numerical Mathematics, vol.54, issue.1, pp.23-37, 2005.
DOI : 10.1016/j.apnum.2004.10.005

F. [. Blanes, A. Casas, and . Murua, Splitting and composition methods in the numerical integration of differential equations, Bol. Soc. Esp. Mat. Apl, vol.45, pp.87-143, 2008.

F. [. Blanes, A. Casas, and . Murua, Splitting methods with complex coefficients, SeMA Journal, vol.159, issue.1, pp.47-61, 2010.
DOI : 10.1007/BF03322541
URL : http://arxiv.org/abs/1001.1549

P. [. Castella, S. Chartier, G. Descombes, and . Vilmart, Splitting methods with complex times for parabolic equations, BIT Numerical Mathematics, vol.150, issue.3, pp.487-508, 2009.
DOI : 10.1007/s10543-009-0235-y
URL : https://hal.archives-ouvertes.fr/hal-00777092

A. [. Creutz and . Gocksch, Higher-order hybrid Monte Carlo algorithms, Physical Review Letters, vol.63, issue.1, pp.9-12, 1989.
DOI : 10.1103/PhysRevLett.63.9

]. J. Cha03 and . Chambers, Symplectic integrators with complex time steps, Astron. J, vol.126, pp.1119-1126, 2003.

A. [. Chartier and . Murua, An algebraic theory of order, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.4, pp.607-630, 2009.
DOI : 10.1051/m2an/2009029
URL : https://hal.archives-ouvertes.fr/hal-00777190

M. [. Descombes and . Schatzman, Strang's formula for holomorphic semi-groups, Journal de Math??matiques Pures et Appliqu??es, vol.81, issue.1, pp.93-114, 2002.
DOI : 10.1016/S0021-7824(01)01216-8
URL : http://doi.org/10.1016/s0021-7824(01)01216-8

]. E. For89 and . Forest, Canonical integrators as tracking codes, AIP Conference Proceedings, vol.184, pp.1106-1136, 1989.

O. [. Fauve and . Thual, Localized structures generated by subcritical instabilities, J. Phys. France, vol.49, pp.1829-1833, 1988.
URL : https://hal.archives-ouvertes.fr/jpa-00210864

C. [. Hairer, G. Lubich, and . Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Series in Computational Mathematics 31, 2006.
DOI : 10.4171/owr/2006/14
URL : https://hal.archives-ouvertes.fr/hal-01403326

]. E. Ho09a, A. Hansen, and . Ostermann, Exponential splitting for unbounded operators, Math. Comp, vol.78, pp.1485-1496, 2009.

]. E. Ho09b, A. Hansen, and . Ostermann, High order splitting methods for analytic semigroups exist, BIT Numerical Analysis, vol.49, pp.527-542, 2009.

H. Holden, K. H. Karlsen, K. A. Lie, and N. H. Risebro, Splitting Methods for Partial Differential Equations with Rough Solutions, 2010.
DOI : 10.4171/078

J. [. Hundsdorfer and . Verwer, Numerical Solution of Time-Dependent Advection-Diffusion- Reaction Equations, 2003.
DOI : 10.1007/978-3-662-09017-6

C. [. Jahnke and . Lubich, Error bounds for exponential operator splittings, Bit Numerical Mathematics, vol.40, issue.4, pp.735-744, 2000.
DOI : 10.1023/A:1022396519656

]. C. Lub08 and . Lubich, On splitting methods for Schrödinger?Poisson and cubic nonlinear Schrödinger equations, Math. Comp, vol.77, pp.2141-2153, 2008.

J. [. Murua and . Sanz-serna, Order conditions for numerical integrators obtained by composing simpler integrators, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.357, issue.1754, pp.1079-1100329, 1962.
DOI : 10.1098/rsta.1999.0365

Q. Sheng, Solving Linear Partial Differential Equations by Exponential Splitting, IMA Journal of Numerical Analysis, vol.9, issue.2, pp.199-212, 1989.
DOI : 10.1093/imanum/9.2.199

]. M. Suz90 and . Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations, Phys. Lett. A, vol.146, pp.319-323, 1990.

M. Suzuki, General theory of fractal path integrals with applications to many???body theories and statistical physics, Journal of Mathematical Physics, vol.32, issue.2, pp.400-407, 1991.
DOI : 10.1063/1.529425

Z. [. Tang and . Teng, Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms, SIAM Journal on Numerical Analysis, vol.32, issue.1, pp.110-127, 1995.
DOI : 10.1137/0732004
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.2390

]. T. Tang98 and . Tang, Convergence Analysis for Operator-Splitting Methods Applied to Conservation Laws with Stiff Source Terms, SIAM Journal on Numerical Analysis, vol.35, issue.5, pp.1939-1968, 1998.
DOI : 10.1137/S0036142996308927

]. M. Tal08 and . Thalhammer, High-order exponential operator splitting methods for time-dependent Schrödinger equations, SIAM J. Numer. Anal, vol.46, pp.2022-2038, 2008.

]. H. Yos90 and . Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A, vol.150, pp.262-268, 1990.