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Akrivis, Georgios; Smyrlis, Yiorgos-Sokratis

Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation. (English) Zbl 1057.65069

Appl. Numer. Math. 51, No. 2-3, 151-169 (2004).
The authors present a computational method for the Kuromoto-Sivashinsky equation. The spatial discretization is by Fourier collocation. For the temporal discretization a 6-th order backward difference method is used for the linear terms, and an explicit Adams method is used for the nonlinear convection term. It is proved that the method converges.
Reviewer: Gerald W. Hedstrom (Pleasanton)

Cited in 2 Reviews
Cited in 35 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Kuromoto-Sivashinsky equation; trigonometric collocation; Fourier collocation; backward difference method; Adams method; implicit-explicit BDF methods; periodic attractors; period doubling cascades

Software:

RODAS
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Full Text: DOI

References:

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