Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods
Chebyshev spectral collocation methods (known as EI-Gendi method [S.E. El-Gendi, Chebyshev Solution of differential integral and integro-differential equations, comput. J. 12 (1969) 282-287; B. Mihaila. I.Mihaila, Numerical approximation using Chebyshev polynomial expansions: El-gendi's method revisited, J. Phys. A 35 (2002) 731-7461) are extended to deal with the generalized Kuramoto-Sivashinsky equation. The problem is reduced to a system of ordinary differential equations that are solved by combinations of backward differential formula and appropriate explicit schemes (implicit-explicit BDF methods [G. Akrivis, Y.S. Smyrlis, Implicit-explicit BDF methods for the l(Kuramoto-Sivashinsky equation, Appl. Numer. Math. 51 (2004) 151-169]). Good numerical results have been obtained and compared with the exact Solutions. (c) 2008 Elsevier Ltd. All rights reserved.
numerical solution kuramoto-sivashinsky equation chebyshev spectral collocation method