The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Hermite pseudospectral method for nonlinear partial differential equations

Ben-Yu Guo; Cheng-Long Xu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 4, page 859-872
  • ISSN: 0764-583X

How to cite

top

Guo, Ben-Yu, and Xu, Cheng-Long. "Hermite pseudospectral method for nonlinear partial differential equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.4 (2000): 859-872. <http://eudml.org/doc/194016>.

@article{Guo2000,
author = {Guo, Ben-Yu, Xu, Cheng-Long},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Hermite polynomial interpolation; pseudospectral method; Burgers equation; stability; convergence; numerical results},
language = {eng},
number = {4},
pages = {859-872},
publisher = {Dunod},
title = {Hermite pseudospectral method for nonlinear partial differential equations},
url = {http://eudml.org/doc/194016},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Guo, Ben-Yu
AU - Xu, Cheng-Long
TI - Hermite pseudospectral method for nonlinear partial differential equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 4
SP - 859
EP - 872
LA - eng
KW - Hermite polynomial interpolation; pseudospectral method; Burgers equation; stability; convergence; numerical results
UR - http://eudml.org/doc/194016
ER -

References

top
  1. [1] R. A. Adams, Sobolev Spaces. Academic Press, New York (1975). Zbl0314.46030MR450957
  2. [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. MR1470226
  3. [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. Zbl0734.73090MR1067965
  4. [4] R. Courant K. O. Friedrichs and H. Levy, Über die partiellen differezengleichungen der mathematischen physik. Math. Annal. 100 (1928) 32-74. Zbl54.0486.01MR1512478JFM54.0486.01
  5. [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. Zbl0842.46017MR1270241
  6. [6] D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions. Math. Comp. 57 (1990) 597-619. Zbl0764.35007MR1094949
  7. [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. Zbl0391.76027MR458929
  8. [8] B. Y. Guo, Generalized stability of discretization and its applications to numerical solution of nonlinear differential equations. Contemp. Math. 163 (1994) 33-54. Zbl0811.65071MR1276073
  9. [9] B. Y. Guo, Spectral Methods and Their Applications. World Scientific, Singapore (1998). Zbl0906.65110MR1641586
  10. [10] B. Y. Guo, Error estimation for Hermite spectral method for nonlinear partial differential equations. Math. Comp. 68 (1999) 1067-1078. Zbl0918.65069MR1627789
  11. [11] A. L. Levin and D. S. Lubinsky, Christoffel functions, orthogonal polynomials, and Nevaiś conjecture for Freud weights. Constr. Approx. 8 (1992) 461-533. Zbl0762.41011MR1194029
  12. [12] D. S. Lubinsky and F. Moricz, The weighted Lp-norm of orthogonal polynormal of Freud weights. J. Approx. Theory 77 (1994) 42-50. Zbl0801.42018MR1273698
  13. [13] Y. Maday, B. Pernaud-Thomas and H. Vandeven, Une réhabilitation des méthodes spectrales de type Laguerre. Rech. Aérospat. 6 (1985) 353-379. Zbl0604.42026MR850680
  14. [14] R. D. Richitmeyer and K. W. Morton, Finite Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York (1967). Zbl0155.47502
  15. [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. Zbl0149.11603MR205495
  16. [16] G. Szegö, Orthogonal Polynomials. Amer. Math. Soc., New York (1967). JFM65.0278.03
  17. [17] A. F. Timan, Theory of Approximation of Functions of a Real Variable. Pergamon Press, Oxford (1963). Zbl0117.29001MR192238

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.