Abstract
The monotonicity of a two-time-level CABARET scheme approximating a multidimensional scalar conservation law is analyzed. A modification of this scheme is proposed. This modification retains the monotonicity of one-dimensional difference solutions to the CABARET scheme in a linear approximation. As a result, it provides an increased smoothness in the calculation of multidimensional discontinuous solutions. The results of test calculations are given. They illustrate the advantages of the modified scheme.
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