Numerical solution of linear time-fractional Kuramoto-Sivashinsky equation via quintic B-splines

Abstract

A numerical scheme is developed to solve the time-fractional linear Kuramoto-Sivahinsky equation in this work. The time-fractional derivative (of order γ) is taken in the Caputo sense. The scheme comprises the backward Euler formula in the temporal direction and the quintic B-spline collocation approach in the spatial direction. Through rigorous analysis, the proposed method is shown to be unconditionally stable and convergent of order $2-\gamma$ and two in the temporal and spatial directions, respectively. Two test problems are solved numerically to demonstrate the convergence and accuracy of the method.

Keywords:

• Caputo derivative
• backward Euler scheme
• time-fractional linear Kuramoto-Sivashinsky equation
• B-splines
• convergence
• error estimates

2000 AMS SUBJECT CLASSIFICATIONS:

• 35R11
• 34K37

Acknowledgments

The authors sincerely thank the reviewers for providing valuable comments to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).