### Abstract

Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system. It is shown that a nonmonotone bicompact scheme has a higher order of convergence in domains of influence of unsteady shock waves. If spurious oscillations are suppressed by applying a conservative limiting procedure, then the bicompact scheme, though being high-order accurate on smooth solutions, has a reduced (first) order of convergence in the domains of influence of shock waves.

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## ACKNOWLEDGMENTS

We are grateful to N.A. Khandeeva, who kindly placed numerical results based on Rusanov’s scheme at our disposal.

## Funding

This work was supported by the Russian Science Foundation, grant no. 16-11-10033.

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Translated by I. Ruzanova

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Bragin, M.D., Rogov, B.V. On the Accuracy of Bicompact Schemes as Applied to Computation of Unsteady Shock Waves.
*Comput. Math. and Math. Phys.* **60, **864–878 (2020). https://doi.org/10.1134/S0965542520050061

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### Keywords:

- hyperbolic system of conservation laws
- bicompact schemes
- shallow water equations
- orders of local and integral convergence