Hermite pseudospectral method for nonlinear partial differential equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 4, p. 859-872
@article{M2AN_2000__34_4_859_0,
     author = {Guo, Ben-Yu and Xu, Cheng-Long},
     title = {Hermite pseudospectral method for nonlinear partial differential equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {34},
     number = {4},
     year = {2000},
     pages = {859-872},
     zbl = {0966.65072},
     mrnumber = {1784489},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_4_859_0}
}
Guo, Ben-Yu; Xu, Cheng-Long. Hermite pseudospectral method for nonlinear partial differential equations. ESAIM: Mathematical Modelling and Numerical Analysis - 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 450957 | Zbl 0314.46030

[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 1470226

[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 1067965 | Zbl 0734.73090

[4] R. Courant K. O. Friedrichs and H. Levy, Über die partiellen differezengleichungen der mathematischen physik. Math. Annal. 100 (1928) 32-74. | JFM 54.0486.01 | MR 1512478

[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 1270241 | Zbl 0842.46017

[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 1094949 | Zbl 0764.35007

[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 458929 | Zbl 0391.76027

[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 1276073 | Zbl 0811.65071

[9] B. Y. Guo, Spectral Methods and Their Applications. World Scientific, Singapore (1998). | MR 1641586 | Zbl 0906.65110

[10] B. Y. Guo, Error estimation for Hermite spectral method for nonlinear partial differential equations. Math. Comp. 68 (1999) 1067-1078. | MR 1627789 | Zbl 0918.65069

[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 1194029 | Zbl 0762.41011

[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 1273698 | Zbl 0801.42018

[13] Y. Maday, B. Pernaud-Thomas and H. Vandeven, Une réhabilitation des méthodes spectrales de type Laguerre. Rech. Aérospat. 6 (1985) 353-379. | MR 850680 | Zbl 0604.42026

[14] R. D. Richitmeyer and K. W. Morton, Finite Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York (1967). | Zbl 0155.47502

[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 205495 | Zbl 0149.11603

[16] G. Szegö, Orthogonal Polynomials. Amer. Math. Soc., New York (1967). | JFM 65.0278.03

[17] A. F. Timan, Theory of Approximation of Functions of a Real Variable. Pergamon Press, Oxford (1963). | MR 192238 | Zbl 0117.29001