Abstract
In this paper we develop a new Fourier pseudospectral method with a restrain operator for the modified Korteweg-de Vries (MKDV) equation. We prove the generalized stability of the scheme, from which the convergence follows.
Recent publications on spectral methods for nonlinear partial differential equations provide new potent techniques (See [1–8]). In many of the relevant papers, pseudospectral methods are used, because they are more efficient than spectral methods (See[9–12]). But sometimes pseudospectral methods have nonlinear instability, so some filtering or smoothing techniques are used (See[13,14]). The authors also proposed a restrain operator for KDV and Burgers equation (See[15, 16]).
In this paper a restrain operator R is used to develop a new Fourier pseudospectral method for the modified Korteweg-de Vries (MKDV) equation. We prove the the generalized stability of the method, from which the convergence follows with some assumption.
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© 1987 Springer-Verlag
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Ma, Hp., Guo, By. (1987). The fourier pseudospectral method with a restrain operator for the M.K.D.V. equation. In: Zhu, YI., Guo, By. (eds) Numerical Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078543
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DOI: https://doi.org/10.1007/BFb0078543
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