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Numerical analysis of pseudospectral methods for the Kuramoto-Sivashinsky equation. (English) Zbl 0806.65122
The Kuramoto-Sivashinsky equation requires the use of numerical simulation when it is used as a model or seen as a mathematically relevant dynamical system. The authors prove the stability and convergence of a pseudospectral technique applied to this equation. Two cases of nonlinear terms are taken to establish the results.
The technique used by the authors can be applied with suitable modification to study pseudospectral discretization of the Burgers equation and more general equations.

MSC:
65Z05 Applications to the sciences
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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