N. Besse and M. Mehrenberger, Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov--Poisson system, Mathematics of Computation, vol.77, issue.261, pp.93-123, 2008.
DOI : 10.1090/S0025-5718-07-01912-6
URL : https://hal.archives-ouvertes.fr/hal-00594785

M. Brunetti, X. Lapillonne, S. Brunner, and T. M. Tran, Comparison of semi-Lagrangian and Eulerian algorithms for solving Vlasov-type equations, colloque numérique suisse, 2008.

J. Carillo and F. Vecil, Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models, SIAM Journal on Scientific Computing, vol.29, issue.3, pp.1179-1206, 2007.
DOI : 10.1137/050644549

P. Colella and P. R. Woodward, The Piecewise Parabolic Method (PPM) for gas-dynamical simulations, Journal of Computational Physics, vol.54, issue.1, pp.174-201, 1984.
DOI : 10.1016/0021-9991(84)90143-8

C. Z. Cheng and G. Knorr, The integration of the vlasov equation in configuration space, Journal of Computational Physics, vol.22, issue.3, pp.330-3351, 1976.
DOI : 10.1016/0021-9991(76)90053-X

N. Crouseilles, T. Respaud, and E. Sonnendrücker, A forward semi- Lagrangian scheme for the numerical solution of the Vlasov equation, INRIA research report, vol.6727, 2008.

C. De-boor, A practical guide to splines, 1978.
DOI : 10.1007/978-1-4612-6333-3

F. Filbet, E. Sonnendrücker, and P. Bertrand, Conservative Numerical Schemes for the Vlasov Equation, Journal of Computational Physics, vol.172, issue.1, pp.166-187, 2001.
DOI : 10.1006/jcph.2001.6818

F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Computer Physics Communications, vol.150, issue.3, pp.247-266, 2003.
DOI : 10.1016/S0010-4655(02)00694-X
URL : https://hal.archives-ouvertes.fr/hal-00129663

A. Ghizzo, P. Bertrand, M. L. Begue, T. W. Johnston, and M. Shoucri, A Hilbert-Vlasov code for the study of high-frequency plasma beatwave accelerator, IEEE Transactions on Plasma Science, vol.24, issue.2, p.370, 1996.
DOI : 10.1109/27.510001

V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet et al., A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation, Journal of Computational Physics, vol.217, issue.2, pp.395-423, 2006.
DOI : 10.1016/j.jcp.2006.01.023
URL : https://hal.archives-ouvertes.fr/hal-00594856

F. Coquel, . Ph, J. Helluy, and . Schneider, Second-order entropy diminishing scheme for the Euler equations, International Journal for Numerical Methods in Fluids, vol.39, issue.9, pp.1029-1061, 2006.
DOI : 10.1002/fld.1104
URL : https://hal.archives-ouvertes.fr/hal-00139605

F. Huot, A. Ghizzo, P. Bertrand, E. Sonnendrücker, and O. Coulaud, Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov???Maxwell system, Journal of Computational Physics, vol.185, issue.2, pp.512-531, 2003.
DOI : 10.1016/S0021-9991(02)00079-7

D. Kershaw, The explicit inverses of two commonly occurring matrices, Mathematics of Computation, vol.23, issue.105, pp.189-191, 1969.
DOI : 10.1090/S0025-5718-1969-0238478-X

J. Laprise and A. , A Class of Semi-Lagrangian Integrated-Mass (SLM) Numerical Transport Algorithms, Monthly Weather Review, vol.123, issue.2, pp.553-565, 1995.
DOI : 10.1175/1520-0493(1995)123<0553:ACOSLI>2.0.CO;2

T. Nakamura, R. Tanaka, T. Yabe, and K. Takizawa, Exactly Conservative Semi-Lagrangian Scheme for Multi-dimensional Hyperbolic Equations with Directional Splitting Technique, Journal of Computational Physics, vol.174, issue.1, pp.171-207, 2001.
DOI : 10.1006/jcph.2001.6888

T. Nakamura and T. Yabe, Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov???Poisson equation in phase space, Computer Physics Communications, vol.120, issue.2-3, pp.122-154, 1999.
DOI : 10.1016/S0010-4655(99)00247-7

M. Shoucri, Nonlinear evolution of the bump-on-tail instability, Physics of Fluids, vol.22, issue.10, p.2038, 1979.
DOI : 10.1063/1.862470

M. Shoucri, A two-level implicit scheme for the numerical solution of the linearized vorticity equation, International Journal for Numerical Methods in Engineering, vol.18, issue.10, p.1525, 1981.
DOI : 10.1002/nme.1620171007

E. Sonnendrücker, J. Roche, P. Bertrand, and A. , The Semi-Lagrangian Method for the Numerical Resolution of the Vlasov Equation, Journal of Computational Physics, vol.149, issue.2, pp.201-220, 1999.
DOI : 10.1006/jcph.1998.6148

R. Tanaka, T. Nakamura, and T. Yabe, Constructing exactly conservative scheme in a non-conservative form, Computer Physics Communications, vol.126, issue.3, pp.232-243, 2000.
DOI : 10.1016/S0010-4655(99)00473-7

T. Umeda, M. Ashour-abdalla, and D. Schriver, Comparison of numerical interpolation schemes for one-dimensional electrostatic Vlasov code, Journal of Plasma Physics, vol.72, issue.06, pp.1057-1060, 2006.
DOI : 10.1017/S0022377806005228

H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, vol.150, issue.5-7, p.262, 1990.
DOI : 10.1016/0375-9601(90)90092-3

M. Zerroukat, N. Wood, and A. Staniforth, A monotonic and positive???definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.611, pp.2923-2936, 2005.
DOI : 10.1256/qj.04.97

M. Zerroukat, N. Wood, and A. Staniforth, The Parabolic Spline Method (PSM) for conservative transport problems, International Journal for Numerical Methods in Fluids, vol.1, issue.11, pp.1297-1318, 2006.
DOI : 10.1002/fld.1154

.. Application-to-the-vlasov-poisson-model, 18 3.4.1 The general algorithm

I. Centre-de-recherche, I. Nancy, ?. Est, and L. , Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès