A collocation method for the Kuramoto-Sivashinsky equation using B-spline

Abstract

In this paper the Kuramoto-Sivashinsky equation is solved
numerically by collocation method. This method is based on a
collocation method using quartic B-spline functions. The applied
numerical method has been shown to be unconditionally stable. To
linearized the non-linear term $uu_x$, we use Taylor series.
The method is applied on some test examples, and the
numerical results have been compared with the exact solutions. The
global relative error in the solutions show the efficiency of the
method computationally.