Abdur Rashid, Abdur Rashid and Md. Ismail, Ahmad Izani (2008) The Fourier Spectral Method For The Sivashinsky Equation. In: Asian Technology Conference In Mathematics, 15-19 December 2008, Suan Sunandha Rajabhat University.
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.
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