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.
Key words:hyperbolic system of conservation laws, bicompact schemes, shallow water equations, orders of local and integral convergence.
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