N. Y. Bakaev, On the bounds of approximations of holomorphic semigroups, BIT Numerical Mathematics, vol.62, issue.4, pp.35-605, 1995.
DOI : 10.1007/BF01739830

P. Brenner and V. Thomée, Stability and Convergence Rates in $L^p$ for Certain Difference Schemes., MATHEMATICA SCANDINAVICA, vol.27, pp.5-23, 1970.
DOI : 10.7146/math.scand.a-10983

P. Brenner and V. Thomée, On Rational Approximations of Semigroups, SIAM Journal on Numerical Analysis, vol.16, issue.4, pp.683-694, 1979.
DOI : 10.1137/0716051

P. R. Chernoff, Note on product formulas for operator semigroups, Journal of Functional Analysis, vol.2, issue.2, pp.238-242, 1968.
DOI : 10.1016/0022-1236(68)90020-7

M. A. Cherif and H. Emamirad, Approximation in the sens of Kato for the transport problem, Elect. J. Diff. Eq, vol.92, pp.1-7, 2009.

M. Crouzeix, Approximation deséquationsdeséquations paraboliques, Ecole d'automnes de Jaca. (see http

M. Crouzeix, S. Larsson, S. Piskarev, and V. Thomée, The stability of rational approximations of analytic semigroups, BIT, vol.18, issue.1, pp.74-84, 1993.
DOI : 10.1007/BF01990345

H. Emamirad and A. , A Functional Calculus Approach for the Rational Approximation with Nonuniform Partitions, Discrete Contin, Dyn. Syst, vol.22, pp.955-972, 2008.

H. J. Hejtmanek, Approximation of Linear Transport Processes, Journal of Mathematical Physics, vol.11, issue.3, pp.995-1000, 1970.
DOI : 10.1063/1.1665236

R. Hersh and T. Kato, High-Accuracy Stable Difference Schemes for Well-Posed Initial-Value Problems, SIAM Journal on Numerical Analysis, vol.16, issue.4, pp.670-682, 1979.
DOI : 10.1137/0716050

T. Kato, Perturbation Theory for Linear Operators Springer?Verlag, 1966.

M. Leroux, Semidiscretization in time for parabolic problems, Mathematics of Computation, vol.33, issue.147, pp.919-931, 1979.
DOI : 10.1090/S0025-5718-1979-0528047-2

C. Palencia, A Stability Result for Sectorial Operators in Banach Bpaces, SIAM Journal on Numerical Analysis, vol.30, issue.5, pp.1373-1384, 1993.
DOI : 10.1137/0730071

C. Palencia, On the stability of variable stepsize rational approximations of holomorphic semigroups, Mathematics of Computation, vol.62, issue.205, pp.93-103, 1994.
DOI : 10.1090/S0025-5718-1994-1201070-9

N. Saito, Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions, Japan Journal of Industrial and Applied Mathematics, vol.43, issue.3, pp.323-337, 2004.
DOI : 10.1007/BF03167586

T. Ushijima, Approximation theory for semigroups of linear operators, Japan J. Math, vol.1, pp.185-224, 1975.

Y. Yan, Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps, BIT Numerical Mathematics, vol.43, issue.3, pp.647-669, 2003.
DOI : 10.1023/B:BITN.0000007061.40742.4e