A 2ND-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 equat ion in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semid iscrete method yields a system of differential algebraic equations (DA Es) of index 1. Error estimates in L-2 and L-infinity norms have been obtained for the semidiscrete approximations. For the temporal discret ization, the time integrator RADAUS is used for the resulting system. Some numerical experiments have been conducted to validate the theoret ical results and to confirm the qualitative behaviors of the Rosenau e quation. Finally, orthogonal cubic spline collocation method is direct ly applied to BBM(Benjamin-Bona-Mahony) and BB MB(Benjamin-Bona-Mahony -Burgers) equations and the well-known decay estimates are demonstrate d for the computed solution. (C) 1998 John Wiley & Sons, Inc.