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

• Published in: Computers & mathematics with applications (1987) Vol. 35; no. 6; pp. 5 - 25
• Main Authors: Manickam, A.V., Moudgalya, K.M., Pani, A.K.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.1998
• Subjects: Differential algebraic equations; Error estimates; Implicit Runge-Kutta methods; Kuramoto-Sivashinsky equation; Orthogonal spline collocation method; Semidiscrete schemes; Orthogonal spline collocation method; Error estimates; Semidiscrete schemes; Kuramoto-Sivashinsky equation; Implicit Runge-Kutta methods; Differential algebraic equations
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/S0898-1221(98)00013-3

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 L 2 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.