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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:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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