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The Fourier pseudospectral method with a restrain operator for the RLW equation. (English) Zbl 0684.65097

The authors consider the periodic problem of the reduced long wave (RLW) equation. Since the accuracy of numerical solutions of both finite element methods and difference methods is limited even for very smooth solutions of the equation, the authors develop a new Fourier pseudospectral method, modifying filtering techniques of H.-O. Kreiss and J. Oliger [SIAM J. Numer. Anal. 16, 421–433 (1979; Zbl 0419.65076)], and of H. Ma and the first author [J. Comput. Phys. 65, 120–137 (1986; Zbl 0589.65077)]. The authors present numerical evidence that the proposed method has advantages of previous methods, and prove in addition the stability and convergence of the scheme.
Reviewer: Ph.Brenner

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

[1] Peregrine, D. H., J. Fluid Mech., 25, 321 (1966)
[2] Abdulloev, Kh. O.; Bogolubsky, I. L.; Makhankov, V. T., Phys. Lett. A, 56, 427 (1976)
[3] Olver, P. J., (Math. Proc. Cambridge Philos. Soc., 85 (1979)), 143
[4] Eilbeck, J. C.; McGuire, G. R., J. Comput. Phys., 19, 43 (1975)
[5] Eilbeck, J. C.; McGuire, G. R., J. Comput. Phys., 23, 63 (1977)
[6] Alexander, M. E.; Morris, J. L., J. Comput. Phys., 30, 428 (1979)
[7] Arnold, D. N.; Douglas, J.; Thomee, V., Math. Comput., 36, 53 (1981)
[8] Wu, H. M.; Guo, B. Y., Math. Numer. Sin., 5, 90 (1983)
[9] Gottlieb, D.; Orzsag, S. A., Numerical Analysis of Spectral Methods, (CBMS-NSF, Regional Conference Series in Applied Mathematics, Vol. 26 (1977))
[10] Pasciak, J. E., SIAM J. Numer. Anal., 19, 142 (1982)
[11] Guo, B. Y.; Manoranian, V. S., IMA-JNA, 5, 307 (1985)
[12] Kreiss, H. O.; Oliger, J., SIAM J. Numer. Anal., 16, 421 (1979)
[13] Kuo, P. Y., J. Comput. Math., 1, 353 (1983)
[14] Ma, H. P.; Guo, B. Y., J. Comput. Phys., 65, 120 (1986)
[15] Guo, B.-Y., Acta Math. Sin., 17, 242 (1974)
[16] Guo, B.-Y., Sci. Sin. A, 25, 702 (1982)
[17] Griffiths, D. F., Bull. Inst. Math. Appl., 12, 210 (1982)
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