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A LOCAL RADIAL BASIS FUNCTIONS BASED APPROACH FOR SOLVING KURAMOTO-SIVASHINSKY (KS) EQUATIONS USING DIFFERENTIAL QUADRATURE

. Aqib Zafar & Aimel Zafar


Abstract

In this article, we have constructed a scheme to calculate the numerical solutions of 1-D nonlinear Kuramoto-Sivashinsky equations. The scheme is created on local radial basis functions (LRBFs) using the differential quadrature (DQ) method. The space derivative is approximated through the RBFs using a central scheme in the neighborhood of a collocation node. Neighborhoods have seven, nine, eleven and fifteen points used in this regard. The LRBFDQ method converts the PDEs to a system of ODEs and is then evaluated by the typical RK-4 method. Some examples are taken to clarify the accuracy and implementation of the planned scheme. The numerical solutions are compared with some existing results; for the accuracy, validity and stability of the proposed scheme, we use error norms   , and Global Relative Error (GRE).

Key words: Radius, quadrature, neighborhood, evaluated, accuracy.

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