Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation

In this paper, a second-order splitting method is applied to the Kuramoto-Sivashinsky equation and then an orthogonal cubic spline collocation procedure is employed to the approximate resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ normals are obtained for the semidiscrete approximation. For the time discretization, the time integrator RADAU5 is used. The results of numerical experiments are presented to validate the theoretical findings.