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A new conservative finite difference scheme for the Rosenau equation. (English) Zbl 1156.65078
The authors propose a three-level conservative finite difference scheme for the KdV like Rosenau equation \(u_{t}+u_{xxxxt}+u_{x}+uu_{x}=0\). The unique solvability of numerical solutions is shown. Error estimates of second order, convergence and stability of the difference scheme are proved.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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