HYBRID QUINTIC B-SPLINE APPROACH FOR THE NUMERICAL SOLUTION OF KURAMOTO-SIVASHINSKY EQUATION

Muhammad Awais; Syed Sarmad Hasan; Muhammad Wakeel

doi:10.71146/kjmr779

Authors

Muhammad Awais The Superior University Lahore, Pakistan. Author
Syed Sarmad Hasan The Superior University Lahore, Pakistan. Author
Muhammad Wakeel The Superior University Lahore, Pakistan. Author

DOI:

https://doi.org/10.71146/kjmr779

Keywords:

Kuramoto–Sivashinsky equation, hybrid quintic B-spline, trigonometric B-spline, collocation method, Crank–Nicolson scheme, Rubin–Graves linearization, stability analysis

Abstract

This article focuses on finding an approximate solution to the Kuramoto–Sivashinsky (KS) equation. Smoothly connected polynomial segments calledB-spline functions are used and controlled by a set of points. The KS equation is a nonlinear fourth-order partial differential equation which has been used extensively to model various phenomena including flame-front instability, thin film flow and phase dynamics. The hybrid basis consists of a convex combination of polynomial quintic B-splines and trigonometric quintic B-splines. The numerical approximation of the time is done by the Crank–Nicolson finite difference method and the linearization of the nonlinear term is realized by the Rubin–Graves technique. The approximation of spatial derivatives is done with HQBS functions. Von Neumann approach is widely used to study the stability of a numerical method. The accuracy and effectiveness of the scheme is confirmed by the numerical results, which are accurate and close to the analytical solutions.

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