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On the Numerical Solution of the Kuramoto-Sivashinsky Equation Using Operator-Splitting Method

JK Djoko*, AA Aderogba, M Chapwanya

An operator-splitting scheme for the Kuramoto-Sivashinsky equation, ut + uux + uxx + uxxxx = 0, is proposed. The method is based on splitting the convective and the diffusive differential terms thereby permitting an efficient scheme choice for each of them, and when combined give a reliable solution for the entire equation. We demonstrate the accuracy and capability of the proposed split scheme via several numerical experiments. Computations of the bound, lim sup ∥u(x; t)∥2 for the equation is also t!1 Presented.