A. T. Benjamin and D. Walton, Combinatorially composing Chebyshev polynomials, Journal of Statistical Planning and Inference, vol.140, issue.8, p.31, 2010.
DOI : 10.1016/j.jspi.2010.01.012

URL : https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1107&context=hmc_fac_pub

J. P. Boyd, Chebyshev and Fourier Spectral Methods, p.27, 2000.
DOI : 10.1007/978-3-642-83876-7

R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, vol.7, p.40, 1998.

Y. K. Cheung, W. G. Jin, and O. C. Zienkiewicz, Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions, Comm. Appl. Num. Meth, vol.5, p.32, 1989.

M. Chhay, D. Dutykh, M. Gisclon, and C. Ruyer-quil, Asymptotic heat transfer model in thin liquid films, p.33, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01224182

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-297, 1965.

J. R. Dormand and P. J. Prince, A family of embedded Runge-Kutta formulae, J. Comp. Appl. Math, vol.6, p.48, 1980.

A. Einstein, Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Annalen der Physik, vol.322, issue.8, p.39, 1905.

A. Einstein, Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes, Die Naturwissenschaften, vol.14, issue.11, p.39, 1926.

L. C. Evans, Partial Differential Equations, p.34, 2010.

B. Fornberg, A practical guide to pseudospectral methods, vol.27, p.43, 1996.

J. Fourier, Théorie analytique de la chaleur, vol.7, p.36, 1822.

M. Gisclon, A propos de l'équation de la chaleur et de l'analyse de Fourier, Le journal de maths des élèves, vol.1, issue.4, p.44, 1998.

D. F. Griffiths, J. W. Dold, and D. J. Silvester, Separation of Variables, Essential Partial Differential Equations, p.44, 2015.

J. Hadamard, Sur les problèmes aux dérivées partielles et leur signification physique. Princeton University Bulletin, p.49, 1902.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration, Spring Series in Computational Mathematics, vol.31, p.46, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01403326

E. Hairer, S. P. Nørsett, and G. Wanner, Solving ordinary differential equations: Nonstiff problems, p.24, 2009.

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and DifferentialAlgebraic Problems, Springer Series in Computational Mathematics, vol.14, p.46, 1996.

I. Herrera, Boundary methods: development of complete systems of solutions, Finite Elements Flow Analysis, p.33, 1982.

I. Herrera, Boundary Methods: An Algebraic Theory, p.33, 1984.

D. J. Higham, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Review, vol.43, issue.3, p.42, 2001.

E. T. Jaynes, Probability Theory, p.40, 2003.

E. Kita and N. Kamiya, Trefftz method: an overview, Advances in Engineering Software, vol.24, p.34, 1995.

H. O. Kreiss and G. Scherer, Method of lines for hyperbolic equations, SIAM Journal on Numerical Analysis, vol.29, p.45, 1992.

B. Lapeyre and J. Lelong, A framework for adaptive Monte-Carlo procedures, Monte Carlo Methods Appl, vol.17, issue.1, p.40, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00448864

N. Mendes and P. C. Philippi, A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients, Int. J. Heat Mass Transfer, vol.48, issue.1, pp.37-51, 2005.

W. F. Osgood, Beweis der Existenz einer Lösung der Differentialgleichung dy dx = f

, ohne Hinzunahme der Cauchy-Lipschitz'schen Bedingung, vol.9, p.51, 1898.

K. Pearson, The Problem of the Random Walk, Nature, vol.72, p.38, 1905.

J. Philibert, One and a half century of diffusion: Fick, Einstein, before and beyond, Diffusion Fundamentals, p.34, 2005.

S. C. Reddy and L. N. Trefethen, Stability of the method of lines, Numerische Mathematik, vol.62, issue.1, p.45, 1992.

W. E. Schiesser, Method of lines solution of the Korteweg-de vries equation, Computers Mathematics with Applications, vol.28, pp.147-154, 1994.

L. F. Shampine, ODE solvers and the method of lines, Numerical Methods for Partial Differential Equations, vol.10, issue.6, p.45, 1994.

L. F. Shampine and M. W. Reichelt, The MATLAB ODE Suite, SIAM Journal on Scientific Computing, vol.18, p.24, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01333731

P. Solin, Partial Differential Equations and the Finite Element Method, vol.12, p.13, 2005.

L. N. Trefethen, Spectral methods in MatLab, Society for Industrial and Applied Mathematics, vol.18, p.26, 2000.

E. Trefftz, Gegenstück zum ritzschen Verfahren, Proc. 2nd Int, p.32, 1926.

H. Uecker, A short ad hoc introduction to spectral methods for parabolic PDE and the NavierStokes equations, vol.18, p.27, 2009.

B. Van-leer, Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes, Commun. Comput. Phys, vol.1, issue.6, pp.192-206, 2006.

P. Vértesi, Optimal Lebesgue constant for Lagrange interpolation, SIAM J. Numer. Anal, vol.27, p.11, 1990.

A. Wintner, On the Convergence of Successive Approximations, American Journal of Mathematics, vol.68, issue.1, p.13, 1946.

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