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A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation. (English) Zbl 0930.65111

A method for the numerical solution of a Korteweg-de Vries-like Rosenau equation is presented. It consists in a second-order splitting of the equation and then an orthogonal cubic spline collocation procedure is applied to approximate the resulting system in the spatial direction. This semidiscrete method, with continuous time, yields a system of differential-algebraic equations of the first order. Error estimates are obtained for the semidiscrete approximation.

For numerical calculations a temporal discretization is used to the approximated system. Some numerical experiments are conducted which confirmed the convergence of solution. Finally, the orthogonal cubic spline collocation method is applied to the Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations and well-known results like decay estimates are derived for the computed solutions.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
65M12Stability and convergence of numerical methods (IVP of PDE)
65M15Error bounds (IVP of PDE)