Quintic B-spline collocation method for numerical solution of the Kuramoto–Sivashinsky equation

Abstract In this paper, the quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto–Sivashinsky equation. The scheme is based on the Crank–Nicolson formulation for time integration and quintic B-spline functions for space integration. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are also shown graphically and are compared with results given in the literature.

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