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Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation. (English) Zbl 1166.65041
The authors consider an initial-boundary value problem of Rosenau-Burgers equation $$u_{t}+u_{xxxxt}-u_{xx}+u_{x}+uu_{x}=0$$ and propose a Crank-Nicolson type finite difference scheme. The existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is stable and convergent in the order of $O(\Delta t^{2}+\Delta x^{2})$. The method is tested by an example. It will be better if the new scheme is tested by a shock wave problem.

##### MSC:
 65M06 Finite difference methods (IVP of PDE) 65M12 Stability and convergence of numerical methods (IVP of PDE) 35Q53 KdV-like (Korteweg-de Vries) equations
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##### References:
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