Spectral method for the diffusion equation with a source term

[1] A. Boutaghou and F.Z. Nouri, On finite spectral method for axi-symmetric elliptic problem, J. Anal. Appl. 4
(2006), no. 3, 149–168.
[2] A. Boutaghou and F.Z. Nouri, Stokes problem in the case of axi-symmetric data and homogeneous boundary
conditions, Far East J. Appl. Math. 21 (2005), no. 2, 219–239.
[3] A. Quarteroni, R. Sacco and F. Saleri, M´ethodes Num´eriques, Algorithmes, Analyse et applications, SpringerVerlag Italia, Milano, 2007.
[4] B. Mercier, Stabilit´e et convergence des m´ethodes spectrales polynomiales: Application `a l’´equation d’avection,
R.A.I.R.O. Anal. num´er. 16 (1982), 97–100.
[5] C. Bernardi and Y. Maday, Approximations spectrales de problemes aux limites elliptiques, Vol. 10. Berlin:
Springer, 1992.
[6] C. Bernardi, M. Dauge, Y. Maday and M. Aza¨ıez, Spectral methods for axisymmetric domains numerical algorithms and tests due to Mejdi Aza¨ıez, Series in Applied Mathematics, Gauthier-Villars, Paris Amsterdam
Lausanne, 1999.
[7] C. Canuto, Spectral methods in fluid dynamics, Springer-Verlag, Berlin; New York, ed. Corr. 2nd print., 1988.[8] D. Gottlieb, The stability of pseudospectral Chebyshev methods, Math. Comput. 36 (1981), 107–118.
[9] D. Gottlieb and S.A. Orszag, Numerical analysis of spectral methods: Theory and applications, Society for Industrial and Applied Mathematics, 1977.
[10] D.J. Acheson, Elementary Fluid Dynamics, Oxford University Press, New York, 1990.
[11] D. Richards, Advanced mathematical methods with Maple, (Cambridge University Press, Cambridge, UK; New
York, 2002.
[12] E.P. Stephan and M. Suri, On the convergences of the p-version of the boundary element Galerkin method, Math.
Compt. 52 (1989), 31–48.
[13] G. Allaire, Analyse Num´erique et Optimisation: Une introduction `a la mod´elisation math´ematique et `a la simulation num´erique, Editions Ecole Polytechnique, 2005.
[14] H.J. Weber and G.B. Arfken, Essential Mathematical Methods for Physicists, Elsevier, Academic Press, San
Diego, 2004.
[15] J. De Frutos and R. Munoz-Sola, Chebyshev pseudospectral collocation for parabolic problems with nonconstant
coefficients, Proc. Third Int. Conf. Spect. High Order Meth., 1996, p. 101–107.
[16] L. Pujo-Menjouet, Introduction aux ´equations diff´erentielles, Universit´e Claude Bernard, Lyon I, France, 1918.
[17] M. Crouzeix and A.L. Mignot, Analyse num´erique des ´equations differentilles, Masson, Paris, 1989.
[18] M. Dauge, Spectral-Fourier method for axi-symmetric problems, Proc. Third Int. Conf. Spect. High Order Meth.,
1996.
[19] M. Gisclon, A propos de l’´equation de la chaleur et de l’analyse de Fourier, J. Math. ´el`eves 1 (1998), no. 4,
190–197.
[20] M.S. Sibony and J.-C. Mardon, Approximations et ´equations diff´erentielles, Hermann, Paris, 1982.
[21] P.G. Ciarlet, Introduction `a l’analyse num´erique matricielle et `a l’optimisation, Dunod, 2007.
[22] P.J. Davis and P. Rabinowitz,Methods of numerical integration, Courier Corporation, 2007.
[23] R. Dautray and J.L. Lions, Analyse math´ematique et calcul num´erique pour les sciences et les techniques, Mason
Paris, tome 3, 1987.
[24] S.A. Orszag, Numerical simulation of incompressible flows within simple boundaries in Galerkin (spectral) representations, Stud. Appl. Math. 50 (1971), 293–327.
[25] S.A. Orszag, Spectral methods for problems in complex geometries, J. Comput. Phys. 37 (1980), 70–92.
[26] S. Larsson and V. Thom´ee, Partial differential equations with numerical methods, Texts in Applied Mathematics,
Springer, Berlin, New York, 2003.
[27] T.N. Phillips and A.R. Davies, On semi-infinite spectral elements for Poisson problems with re-entrant boundary
singularities, J. Comput. Apll. Math. 21 (1988), 173–188.
[28] V.I. Smirnov and J. Sislian, Cours de mathematiques superieures, Tome iii-deuxieme partie, 1972.