eng Science and Education Publishing American Journal of Numerical Analysis 2372-2126 2014-04-22 2 3 90 97 10.12691/ajna-2-3-5 AJNA2014235 article Gentian Zavalani zavalanigentian@hotmail.com 1 Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania 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. http://pubs.sciepub.com/ajna/2/3/5/ajna-2-3-5.pdf discrete Fourier transform exponential time differencing exponential time differencing Runge Kutta methods Cauchy integral Kuramoto-Sivashinsky equation