Abstract
The Runge-Kutta discontinuous Galerkin method (RKDG method) is widely used nowadays. The RKDG method is characterized by a high-order accurate solution. As is well known, for ensuring the monotonic solution by this method, it is necessary to use slope limiters. In particular, it is necessary when the solution contains strong discontinuities. However, the application of limiters can negatively affect the accuracy of the solution. In this paper a way of saving the order of accuracy of the solution and ensuring its monotony is investigated.
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