A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation

A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin-Bona-Mahony) and BBMB (Benjamin-Bona-Mahony-Burgers) equations and the well-known decay estimates are demonstrated for the computed solution