Numerical solutions of the generalized Kuramoto–Sivashinsky equation by Chebyshev spectral collocation methods

✍ Scribed by A.H. Khater; R.S. Temsah

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 419 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2008.03.013

✦ Synopsis

Chebyshev spectral collocation methods (known as El-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) 731-746]) 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 Kuramoto-Sivashinsky equation, Appl. Numer. Math. 51 (2004) 151-169]). Good numerical results have been obtained and compared with the exact solutions.