D. Aregba-driollet, M. Briani, and R. Natalini, Asymptotic High-Order Schemes for $2\times2$ Dissipative Hyperbolic Systems, SIAM Journal on Numerical Analysis, vol.46, issue.2, pp.869-894, 2008.
DOI : 10.1137/060678373

. O. Bgm-+-88-]-m, R. Bristeau, B. Glowinski, J. Mantel, G. S. Periaux et al., On the use of subcycling for solving the compressible Navier-Stokes equations by operator-splitting and finite element methods, Communications in Applied Numerical Methods, vol.4, issue.3, pp.309-317, 1988.

L. Greg, . Bryan, L. Michael, . Norman, W. Brian et al., Enzo: An adaptive mesh refinement code for astrophysics, The Astrophysical Journal Supplement Series, vol.14, issue.2112, p.19, 2014.

I. [. Csomós and . Faragó, Error analysis of the numerical solution of split differential equations, Mathematical and Computer Modelling, vol.48, issue.7-8, pp.1090-1106, 2008.
DOI : 10.1016/j.mcm.2007.12.014

P. Csomós, I. Faragó, and . Havasi, Weighted sequential splittings and their analysis, Computers & Mathematics with Applications, vol.50, issue.7, pp.1017-1031, 2005.
DOI : 10.1016/j.camwa.2005.08.004

J. A. Carrillo, T. Goudon, and P. Lafitte, Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes, Journal of Computational Physics, vol.227, issue.16, pp.7929-7951, 2008.
DOI : 10.1016/j.jcp.2008.05.002
URL : https://hal.archives-ouvertes.fr/hal-00768398

J. A. Carrillo, T. Goudon, P. Lafitte, F. Crandall, and T. M. Liggett, Numerical Schemes of Diffusion Asymptotics and??Moment Closures for Kinetic Equations, Journal of Scientific Computing, vol.1, issue.1, pp.113-149265, 1971.
DOI : 10.1007/s10915-007-9181-5
URL : https://hal.archives-ouvertes.fr/hal-00768401

]. W. Dan98 and . Daniel, A study of the stability of subcycling algorithms in structural dynamics, Computer Methods in Applied Mechanics and Engineering, vol.156, pp.1-41, 1998.

]. W. Dan03 and . Daniel, A partial velocity approach to subcycling structural dynamics, Computer Methods in Applied Mechanics and Engineering, vol.192, pp.375-394, 2003.

M. [. Diaz and . Grote, Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.1985-2014, 2009.
DOI : 10.1137/070709414
URL : https://hal.archives-ouvertes.fr/inria-00193160

P. Godillon-lafitte and T. Goudon, A Coupled Model for Radiative Transfer: Doppler Effects, Equilibrium, and Nonequilibrium Diffusion Asymptotics, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1245-1279, 2005.
DOI : 10.1137/040621041
URL : https://hal.archives-ouvertes.fr/hal-00785328

T. [. Grote and . Mitkova, Explicit local time-stepping methods for Maxwell???s equations, Journal of Computational and Applied Mathematics, vol.234, issue.12, pp.3283-3302, 2010.
DOI : 10.1016/j.cam.2010.04.028

T. [. Grote and . Mitkova, High-order explicit local time-stepping methods for damped wave equations, Journal of Computational and Applied Mathematics, vol.239, pp.270-289, 2013.
DOI : 10.1016/j.cam.2012.09.046

G. [. Hairer and . Wanner, Solving ordinary differential equations II: Stiff and differential-algebraic problems, 2004.

]. S. Jin99 and . Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599

]. S. Jin10 and . Jin, Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review . Lecture Notes for Summer School on " Methods and Models of Kinetic Theory, M&MKT), 2010.

M. Lemou and L. Mieussens, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.334-368, 2008.
DOI : 10.1137/07069479X
URL : https://hal.archives-ouvertes.fr/hal-00348594

]. R. Mcl02 and . Mclachlan, Families of high-order composition methods, Numerical Algorithms, vol.31, issue.1- 4, pp.233-246, 2002.

]. S. Pip97 and . Piperno, Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2d inviscid aeroelastic simulations, International Journal for Numerical Methods in Fluids, vol.25, issue.10, pp.1207-1226, 1997.

A. Mark, K. J. Taylor, . Evans, J. James, P. Hack et al., Subcycled dynamics in the spectral community atmosphere model version 4, Proc. SciDAC, 2010.

]. R. Tem96 and . Temam, Multilevel methods for the simulation of turbulence. A simple model, Journal of Computational Physics, vol.127, issue.2, pp.309-315, 1996.