A. Bayliss, D. Gottlieb, B. J. Matkowsky, and M. Minkoff, An adaptive pseudo-spectral method for reaction diffusion problems, Journal of Computational Physics, vol.81, issue.2, pp.421-443, 1989.
DOI : 10.1016/0021-9991(89)90215-5

J. P. Boyd, The arctan/tan and Kepler-Burgers mappings for periodic solutions with a shock, front, or internal boundary layer, Journal of Computational Physics, vol.98, issue.2, pp.181-193, 1992.
DOI : 10.1016/0021-9991(92)90136-M

P. John and . Boyd, Chebyshev and Fourier spectral methods, 2001.

C. Canuto, A. Hussaini, . Quarteroni, A. Thomas, and . Zang, Spectral methods in fluid dynamics, 1988.
DOI : 10.1007/978-3-642-84108-8

E. Fattal, R. Baer, and R. Kosloff, Phase space approach for optimizing grid representations: The mapped Fourier method, Physical Review E, vol.53, issue.1, pp.1217-1227, 1996.
DOI : 10.1103/PhysRevE.53.1217

S. Futatani, G. Huijsmans, A. Loarte, L. R. Baylor, N. Commaux et al., Non-linear MHD modelling of ELM triggering by pellet injection in DIII-D and implications for ITER, Nuclear Fusion, vol.54, issue.7, p.54073008, 2014.
DOI : 10.1088/0029-5515/54/7/073008

H. Guillard and R. Peyret, On the use of spectral methods for the numerical solution of stiff problems, Computer Methods in Applied Mechanics and Engineering, vol.66, issue.1, pp.17-43, 1988.
DOI : 10.1016/0045-7825(88)90058-8
URL : https://hal.archives-ouvertes.fr/inria-00076001

P. Parks, J. Re, and . Turnbull, Effect of transonic flow in the ablation cloud on the lifetime of a solid hydrogen pellet in a plasma, Physics of Fluids, vol.21, issue.10, pp.1735-1741, 1958.
DOI : 10.1063/1.862088

R. Samtaney, P. Sc-jardin, . Colella, F. Daniel, and . Martin, 3D adaptive mesh refinement simulations of pellet injection in tokamaks, Computer Physics Communications, vol.164, issue.1-3, pp.220-228, 2004.
DOI : 10.1016/j.cpc.2004.06.032

J. Shen and L. Wang, Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.326-349, 2004.
DOI : 10.1137/S0036142903422065

J. Shen and L. Wang, Error analysis for mapped jacobi spectral methods, J. Sci. Comput, vol.24, pp.183-218, 2005.