Error analysis for spectral approximation of the Korteweg-de Vries equation

Y. Maday; A. Quarteroni

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 3, page 499-529
  • ISSN: 0764-583X

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Maday, Y., and Quarteroni, A.. "Error analysis for spectral approximation of the Korteweg-de Vries equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.3 (1988): 499-529. <http://eudml.org/doc/193540>.

@article{Maday1988,
author = {Maday, Y., Quarteroni, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Korteweg-de Vries equation; conservation; convergence; spectral Fourier methods; collocation pseudospectral method; spectral Galerkin method},
language = {eng},
number = {3},
pages = {499-529},
publisher = {Dunod},
title = {Error analysis for spectral approximation of the Korteweg-de Vries equation},
url = {http://eudml.org/doc/193540},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Maday, Y.
AU - Quarteroni, A.
TI - Error analysis for spectral approximation of the Korteweg-de Vries equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 3
SP - 499
EP - 529
LA - eng
KW - Korteweg-de Vries equation; conservation; convergence; spectral Fourier methods; collocation pseudospectral method; spectral Galerkin method
UR - http://eudml.org/doc/193540
ER -

References

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  1. [1] C. BARDOS, Historique sommaire de l'équation de Korteweg-de Vries. Un exemple de l'interaction entre les mathématiques pures et appliques ; Publ. n°45 (1983), Université deParis Nord. MR828857
  2. [2] C. BARDOS, Ondes solitaires et solitons ; Boll. U.M.I. 5, 16-A(1979), pp. 21-47. Zbl0402.35078MR530128
  3. [3] J. L. BONA, V. A. DOUGALIS & O. A. KARAKASHIAN, Fully discrete Galerkin methods for the Korteweg-de Vries équation, to appear in Comput. and Math. with applications 12 A. Zbl0597.65072MR855787
  4. [4] J. L. BONA, W. G. PRITCHARD & L. R. SCOTT, Numerical schemes for a model nonlinear, dispersive wave ; to appear in J. Comput. Phys. Zbl0578.65120MR805869
  5. [5] J. L. BONA & R. SMITH, The nitial value problem for the Korteweg-de Vries equations ; Phil. Roy. Soc. London, 278 (1975), pp. 555-604. Zbl0306.35027MR385355
  6. [6] C. CANUTO, M. Y. HUSSAINI, A. QUARTERONI & T. A. ZANG, Spectral Methods in Fluid Dynamics ; Springer-Verlag, Berlin, 1988. Zbl0658.76001MR917480
  7. [7] T. F. CHAN & T. KERKHOVEN, Fourier methods with extended stability intervals for the Korteweg-de Vries equation; S.I.A.M. J. Numer. Anal. 22 (1985), pp. 441-454. Zbl0571.65082MR787569
  8. [8] B. FORNBERG, Numerical computation of nonlinear waves ; Technical Report Plenum, Nonlinear Phenomena in Physics and Biology (1981). Zbl0525.65074MR749954
  9. [9] B. FORNBERG & F. R. S. WHITHAM, A numerical and theoretical study of certain nonlinear phenomena ; Phil. Trans. Roy. Soc. 289 (1978), pp. 373-404. Zbl0384.65049MR497916
  10. [10] D. JACKSON, The Theory of Approximation, A.M. S. Colloquium publications, vol. XI (1930), New York. Zbl56.0936.01JFM56.0936.01
  11. [11] D. J. KORTEWEG & G. DE VRIES, On the change of form of long waves advancing in rectangular canal, and on a new type of long stationary waves ; Philos. Mag. (1895), pp. 422-443. Zbl26.0881.02JFM26.0881.02
  12. [12] J. L. LIONS & E. MAGENES, Honhomogeneous Boundary Value Problems and Applications, Vol. I, Springer Verlag (1972), Berlin, Heildelberg and New-York. Zbl0223.35039
  13. [13] M. HE PING & G. BEN YU, The Fourier pseudospectral method with a restrain operator for the Korteweg-deVries equation, J. Comp. Phys. 65 (1986), pp. 120-137. Zbl0589.65077MR848450
  14. [14] R. M. MURA, Korteweg-de Vries equation and generalization. I. A remarkable explicit nonlinear transformation ; J. Math. Phys. 9 (1968), pp. 1202-1204. Zbl0283.35018MR252825
  15. [15] R. M. MUIRA, The Korteweg-de Vries equation : A survey of results ; S.I.A.M. Review 18 (1976), pp. 412-459. Zbl0333.35021
  16. [16] R. M. MIURA, C. S. GARDNER & M. D. KRUSKAL ; Korteweg-de Vries equation and generalization. II. Existence of conservation laws and constants of motion ; J. Math. Phys. 9 (1968), pp. 1204-1209. Zbl0283.35019MR252826
  17. [17] J. E. PASCIAK, Spectral and pseudo-spectral methods for advection equation ; Math. comput. 35 (1980), pp. 1081-1092. Zbl0448.65071MR583488
  18. [18] J. E. PASCIAK, Spectral method for a nonlinear initial value problem involving pseudo-differential operators ; S.I.A.M. J. Numer. Maths., 19, 1982, pp. 142-154. Zbl0489.65061MR646600
  19. [19] A. QUARTERONI, Fourier spectral methods for pseudo-parabolic equations ; S.I.A.M. J. Numer. Anal. 24 (1987), pp. 323-335. Zbl0621.65120MR881367
  20. [20] H. SCHAMEL & K. ELSÄSSER, The application of spectral method to nonlinear wave propagation, J. Comp. Phys. 22 (1976), pp. 501-516. Zbl0344.65055MR449164
  21. [21] F. TAPPERT, Numerical solution of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method, in Lecture in Nonlinear wave Motion, A.C. Newell, ed., Applied Mathematics, vol. 15,A.M.S., Providence, Rhode Island (1974), pp. 215-217. Zbl0292.35046
  22. [22] R. TÉMAM, Sur un problème non linéaire; J. Math. Pures Appl. 48 (1969), pp. 159-172. Zbl0187.03902MR261183

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