Generation of the trigonometric cubic B-spline collocation solutions for the Kuramoto-Sivashinsky(KS) equation

A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky(KS) equation. Altough Trigonometric Cubic B-spline(TCB) function is continuous derivatives up to order 2, KS equation is splitted into a coupled system of equation including the first and second order derivatives to be able to the TCB collocation method. Crank-Nicolson method is applied for the time integration of the space discretized system resulted by TCB–spline approach. Some initial boundary value problems are solved to show the validity of the proposed method.