2ND-ORDER SPLITTING COMBINED WITH ORTHOGONAL CUBIC SPLINE COLLOCATIONMETHOD FOR THE KURAMOTO-SIVASHINSKY EQUATION

In this paper, a second-order splitting method is applied to the Kuram oto-Sivashinsky equation and then an orthogonal cubic spline collocati on procedure is employed to the approximate resulting system. This sem idiscrete method yields a system of differential algebraic equations ( DAEs) of index 1. Error estimates in L-2 and L-infinity norms are obta ined for the semidiscrete approximation. For the time discretization, the time integrator RADAU5 is used. The results of numerical experimen ts are presented to validate the theoretical findings.