The Fourier Spectral Method For The Sivashinsky Equation. - Abdur Rashid, Abdur Rashid; Md. Ismail, Ahmad Izani (2008)

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In this paper, a Fourier spectral method for solving the Sivashinsky equation with periodic boundary conditions is developed. We establish semi-discrete and fully discrete schemes of the Fourier spectral method. A fully discrete scheme is constructed in such a way that the linear part is treated implicitly and the nonlinear part explicitly. We use an energy estimation method to obtain error estimates for the approximate solutions. We also perform some numerical experiments.