Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation

Gentian Zavalani^1,

¹Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania

Cite this paper:
Gentian Zavalani. Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation. American Journal of Numerical Analysis. 2014; 2(3):90-97. doi: 10.12691/ajna-2-3-5

Abstract

In this paper we present a numerical technique for solving Kuramoto-Sivashinsky equation, based on spectral Fourier methods. This equation describes reaction diffusion problems, and the dynamics of viscous-fuid films flowing along walls. After we wrote the equation in Fourier space, we get a system. In this case, the exponential time differencing methods integrate the system very much more accurately than other methods since the exponential time differencing methods assume in their derivation that the solution varies slowly in time. When evaluating the coefficients of the exponential time differencing and the exponential time differencing Runge Kutta methods via the”Cauchy integral”. All computational work is done with Matlab package.

Keywords:
discrete Fourier transform exponential time differencing exponential time differencing Runge Kutta methods Cauchy integral Kuramoto-Sivashinsky equation

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