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A recent type of B-spline functions, namely trigonometric cubic B-splines,are adapted to the collocation method for the numerical solutions of theKuramoto-Sivashinsky equation. Having only first and second order derivativesof the trigonometric cubic B-splines at the nodes forces us to convert theKuramoto-Sivashinsky equation to a coupled system of equations by reducing theorder of the higher order terms. Crank-Nicolson method is applied for the timeintegration of the space discretized system resulted by trigonometric cubicB-spline approach. Some initial boundary value problems are solved to show thevalidity of the proposed method.

Generation of the Trigonometric Cubic B-Spline Collocation Solutions for the Kuramoto-Sivashinsky(KS) Equation