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 and two in the temporal and spatial directions, respectively. Two test problems are solved numerically to demonstrate the convergence and accuracy of the method.