An approximate solution to an initial boundary value problem: Rakib–Sivashinsky equation

Abstract

The construction of an approximate solution to an initial boundary value problem for the Rakib–Sivashinsky equation is of concern. The Fourier method is combined with the Adomian decomposition method in order to provide the approximate solution. The variables are separated by the Fourier method and the approximate solution to the nonlinear system of ordinary differential equations is obtained by the Adomian decomposition method. One example of application is presented.

Keywords:

• Rakib–Sivashinsky equation
• Fourier method
• Adomian polynomials
• initial boundary value problem

2009 AMS Subject Classifications::

• 34A34
• 35K15
• G.1.8
• G4

Acknowledgement

This work was partially supported by FCT under the pluriannual founding of unit 212-CMUBI.