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-In this paper we propose a finite difference scheme of second-order approximation, which is a generalization of the familiar Harten scheme to the case of nonstationary adaptive grids. We obtain the conditions under which the scheme satisfies the TVD condition. We test the constructed scheme, using the systems of shallow water equations and gas dynamics equations as an example. In the framework of the nonlinear dispersive Zheleznyak-Pelinovskii model we simulate the process of interaction of an undular bore with a wall.

TVD scheme of second-order approximation on a nonstationary adaptive grid for hyperbolic systems