Stability of a class of nonlocal schemes (Q1116666)

The paper is devoted to a class of stable (in certain sense) finite- difference schemes which are monotonous and divergent and approximate the following evolution equation of the first order \[ (1)\quad \partial u/\partial t+\sum^{n}_{s=1}\partial \phi_ s(u)/\partial x_ s=0. \] Monotony is studied by way of reducing the initial scheme to an equivalent one with a nonlocal stencil. Convergence of the finite- difference solutions to the weak solution of (1) is proved.