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

A numerical scheme is developed to solve the time-fractional linear Kuramoto-Sivahinsky equation in this work. The time-fractional derivative (of order ?) 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 - ? and two in the temporal and spatial directions, respectively. Two test problems are solved numerically to demonstrate the convergence and accuracy of the method.