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A Quintic B-Spline Based Differential Quadrature Method for Numerical Solution of Kuramoto-Sivashinsky Equation

  • R. C. Mittal and Sumita Dahiya EMAIL logo

Abstract

In this paper, the Kuramoto-Sivashinsky equation is solved numerically by implementing a new differential quadrature technique that uses quintic B-spline as the basis functions for space integration. The derivatives are approximated using differential quadrature method. The weighting coefficients are obtained by semi-explicit algorithm including an algebraic system with penta-diagonal coefficient matrix that is solved using the five-band Thomas algorithm. Stability analysis of method has also been done. The accuracy of the proposed scheme is demonstrated by applying on five test problems. Some theoretical properties of KS equation like periodicity, monotonicity and dissipativity etc. have also been discussed. The results are also shown graphically to demonstrate the accuracy and capabilities of this method and comparative study is done with results available in literature. The computed results are found to be in good agreement with the analytical solutions.

MSC 2010: 65Lxx; 65Mxx; 65Nxx; 65Yxx; 65Zxx

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Received: 2015-12-14
Accepted: 2016-12-29
Published Online: 2017-2-15
Published in Print: 2017-4-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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