@article{M2AN_1988__22_3_499_0, author = {Maday, Y. and Quarteroni, A.}, title = {Error analysis for spectral approximation of the Korteweg-de Vries equation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {22}, year = {1988}, pages = {499-529}, mrnumber = {958881}, zbl = {0647.65082}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1988__22_3_499_0} }
Maday, Y.; Quarteroni, A. Error analysis for spectral approximation of the Korteweg-de Vries equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988) pp. 499-529. http://gdmltest.u-ga.fr/item/M2AN_1988__22_3_499_0/
[1] 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. | MR 828857
,[2] Ondes solitaires et solitons ; Boll. U.M.I. 5, 16-A(1979), pp. 21-47. | MR 530128 | Zbl 0402.35078
,[3] Fully discrete Galerkin methods for the Korteweg-de Vries équation, to appear in Comput. and Math. with applications 12 A. | MR 855787 | Zbl 0597.65072
, & ,[4] Numerical schemes for a model nonlinear, dispersive wave ; to appear in J. Comput. Phys. | MR 805869 | Zbl 0578.65120
, & ,[5] The nitial value problem for the Korteweg-de Vries equations ; Phil. Roy. Soc. London, 278 (1975), pp. 555-604. | MR 385355 | Zbl 0306.35027
& ,[6] Spectral Methods in Fluid Dynamics ; Springer-Verlag, Berlin, 1988. | MR 917480 | Zbl 0658.76001
, , & ,[7] Fourier methods with extended stability intervals for the Korteweg-de Vries equation; S.I.A.M. J. Numer. Anal. 22 (1985), pp. 441-454. | MR 787569 | Zbl 0571.65082
& ,[8] Numerical computation of nonlinear waves ; Technical Report Plenum, Nonlinear Phenomena in Physics and Biology (1981). | MR 749954 | Zbl 0525.65074
,[9] A numerical and theoretical study of certain nonlinear phenomena ; Phil. Trans. Roy. Soc. 289 (1978), pp. 373-404. | MR 497916 | Zbl 0384.65049
& ,[10] The Theory of Approximation, A.M. S. Colloquium publications, vol. XI (1930), New York. | JFM 56.0936.01
,[11] 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. | JFM 26.0881.02
& ,[12] Honhomogeneous Boundary Value Problems and Applications, Vol. I, Springer Verlag (1972), Berlin, Heildelberg and New-York. | Zbl 0223.35039
& ,[13] The Fourier pseudospectral method with a restrain operator for the Korteweg-deVries equation, J. Comp. Phys. 65 (1986), pp. 120-137. | MR 848450 | Zbl 0589.65077
& ,[14] Korteweg-de Vries equation and generalization. I. A remarkable explicit nonlinear transformation ; J. Math. Phys. 9 (1968), pp. 1202-1204. | MR 252825 | Zbl 0283.35018
,[15] The Korteweg-de Vries equation : A survey of results ; S.I.A.M. Review 18 (1976), pp. 412-459. | Zbl 0333.35021
,[16] Korteweg-de Vries equation and generalization. II. Existence of conservation laws and constants of motion ; J. Math. Phys. 9 (1968), pp. 1204-1209. | MR 252826 | Zbl 0283.35019
, & ;[17] Spectral and pseudo-spectral methods for advection equation ; Math. comput. 35 (1980), pp. 1081-1092. | MR 583488 | Zbl 0448.65071
,[18] Spectral method for a nonlinear initial value problem involving pseudo-differential operators ; S.I.A.M. J. Numer. Maths., 19, 1982, pp. 142-154. | MR 646600 | Zbl 0489.65061
,[19] Fourier spectral methods for pseudo-parabolic equations ; S.I.A.M. J. Numer. Anal. 24 (1987), pp. 323-335. | MR 881367 | Zbl 0621.65120
,[20] The application of spectral method to nonlinear wave propagation, J. Comp. Phys. 22 (1976), pp. 501-516. | MR 449164 | Zbl 0344.65055
& ,[21] 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. | Zbl 0292.35046
,[22] Sur un problème non linéaire; J. Math. Pures Appl. 48 (1969), pp. 159-172. | MR 261183 | Zbl 0187.03902
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