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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 equation. Having only first and second order derivatives of the trigonometric cubic B-splines at the nodes forces us to convert the Kuramoto-Sivashinsky equation to a coupled system of equations by reducing the order of the higher order terms. Crank-Nicolson method is applied for the time integration of the space discretized system resulted by trigonometric cubic B-spline approach. Some initial boundary value problems are solved to show the validity of the proposed method.

preprint2016arXivOpen access
Ozlem Ersoy Hepson
math.NA
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Ozlem Ersoy Hepson

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