Vol.25, Special Issue A, 2025, pp. S57–S65
https://doi.org/10.69644/ivk-2025-siA-0057  

NUMERICAL SOLUTION OF FOURTH ORDER GENERALISED KURAMOTO-SIVASHINSKY EQUATION USING MODIFIED QUINTIC B-SPLINE DIFFERENTIAL QUADRATURE METHOD

Susan Ishwarya A.1 , Rachna Bhatia1* , Pallavi Mishra1 , Predrag S. Stanimirović2

1) Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, INDIA

S. Ishwarya A. https:/orcid.org/0009-0004-2810-5952 ; R. Bhatia https:/orcid.org/0000-0002-1976-9632 ;

P. Mishra https:/orcid.org/0000-0001-8014-7464 , *email: rachna.bhatia@vit.ac.in 

2) University of Niš, Faculty of Sciences and Mathematics, Niš, SERBIA

P.S. Stanimirović https:/orcid.org/0000-0003-0655-3741 

 

Abstract

In this paper, numerical solutions of the nonlinear generalised Kuramoto-Sivashinsky equation are presented using a modified quintic B-spline differential quadrature method. The Crank-Nicolson and forward finite difference schemes are applied for discretization, while the Rubin and Graves approach is utilised for linearization. The matrix stability approach is used to analyse the method’s stability. Numerical examples demonstrate the accuracy of the method. The computed results are presented in tables and graphs along with a comparative analysis with previous results. The obtained numerical results demonstrate the method’s reliability and its compatibility with the exact solutions.

Keywords: modified quintic B-spline, differential quadrature method, extended Fisher-Kolmogorov equation, Kuramoto-Sivashinsky equation, matrix stability method

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