Generation of the Trigonometric Cubic B-Spline Collocation Solutions for the Kuramoto-Sivashinsky(KS) Equation
This is an incremental method adaptation for numerical solutions of a specific PDE, offering no clear advantage over existing methods.
The authors adapt trigonometric cubic B-splines to a collocation method for solving the Kuramoto-Sivashinsky equation, converting it to a coupled system and using Crank-Nicolson for time integration. They demonstrate validity on initial boundary value problems but provide no concrete numerical results.
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.