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An energy-stable pseudospectral scheme for Swift-Hohenberg equation with its Lyapunov functional

ABSTRACT
We analyze a first order in time Fourier pseudospectral scheme for Swift-Hohenberg equation. One major challenge for the higher order diffusion nonlinear systems is how to ensure the unconditional energy stability and we propose an efficient scheme for the equation based on the convex splitting of the energy. Theoretically, the energy stability of the scheme is proved. Moreover, following the derived aliasing error estimate, the convergence analysis in the discrete l2 -norm for the proposed scheme is given.
KEYWORDS
PAPER SUBMITTED: 2018-06-12
PAPER REVISED: 2018-09-20
PAPER ACCEPTED: 2018-11-25
PUBLISHED ONLINE: 2019-06-08
DOI REFERENCE: https://doi.org/10.2298/TSCI180612249Z
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