no. 4
Hermite pseudospectral method for nonlinear partial differential equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 4, pp. 859-872. 
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     author = {Guo, Ben-Yu and Xu, Cheng-Long},
     title = {Hermite pseudospectral method for nonlinear partial differential equations},
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     pages = {859--872},
     publisher = {Dunod},
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     year = {2000},
     mrnumber = {1784489},
     zbl = {0966.65072},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_4_859_0/}
}
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Guo, Ben-Yu; Xu, Cheng-Long. Hermite pseudospectral method for nonlinear partial differential equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 4, pp. 859-872. http://www.numdam.org/item/M2AN_2000__34_4_859_0/

[1] R. A. Adams, Sobolev Spaces. Academic Press, New York (1975). | MR | Zbl

[2] C. Bernardi and Y. Maday, Spectral methods, in Techniques of Scientific Computing, Part 2, P.G. Ciarlet and J.L. Lions Eds., Elsevier, Amsterdam (1997) 209-486. | MR

[3] O. Coulaud, D. Funaro and O. Kavian, Laguerre spectral approximation of elliptic problems in exterior domains. Comp. Mech. Appl. Mech. Eng. 80 (1990) 451-458. | MR | Zbl

[4] R. Courant K. O. Friedrichs and H. Levy, Über die partiellen differezengleichungen der mathematischen physik. Math. Annal. 100 (1928) 32-74. | JFM | MR

[5] D. Funaro, Estimates of Laguerre spectral projectors in Sobolev spaces, in Orthogonal Polynomials and Their Applications, C. Brezinski, L. Gori and A. Ronveaux Eds., Scientific Publishing Co. (1991) 263-266. | MR | Zbl

[6] D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions. Math. Comp. 57 (1990) 597-619. | MR | Zbl

[7] B. Y. Guo, A class of difference schemes of two-dimensional viscous fluid flow. TR. SUST (1965). Also see Acta. Math. Sinica. 17 (1974) 242-258. | MR | Zbl

[8] B. Y. Guo, Generalized stability of discretization and its applications to numerical solution of nonlinear differential equations. Contemp. Math. 163 (1994) 33-54. | MR | Zbl

[9] B. Y. Guo, Spectral Methods and Their Applications. World Scientific, Singapore (1998). | MR | Zbl

[10] B. Y. Guo, Error estimation for Hermite spectral method for nonlinear partial differential equations. Math. Comp. 68 (1999) 1067-1078. | MR | Zbl

[11] A. L. Levin and D. S. Lubinsky, Christoffel functions, orthogonal polynomials, and Nevaiś conjecture for Freud weights. Constr. Approx. 8 (1992) 461-533. | MR | Zbl

[12] D. S. Lubinsky and F. Moricz, The weighted Lp-norm of orthogonal polynormal of Freud weights. J. Approx. Theory 77 (1994) 42-50. | MR | Zbl

[13] Y. Maday, B. Pernaud-Thomas and H. Vandeven, Une réhabilitation des méthodes spectrales de type Laguerre. Rech. Aérospat. 6 (1985) 353-379. | MR | Zbl

[14] R. D. Richitmeyer and K. W. Morton, Finite Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York (1967). | Zbl

[15] H. J. Stetter, Stability of nonlinear discretization algorithms, in Numerical Solutions of Partial Differential Equations, J. Bramble Ed., Academic Press, New York (1966) 111-123. | MR | Zbl

[16] G. Szegö, Orthogonal Polynomials. Amer. Math. Soc., New York (1967). | JFM

[17] A. F. Timan, Theory of Approximation of Functions of a Real Variable. Pergamon Press, Oxford (1963). | MR | Zbl