Several explicit second- and higher-order difference schemes for the hyperbolic conservation laws with the use of the expansions of grid functions in Lagrange-Burmann series are proposed. Based on the numerical results for a number of one- and two-dimensional test problems, it is shown that, in the case of the Euler equations of an inviscid compressible gas, the quasimonotone profiles of the numerical solutions can be obtained. When solving the steady two-dimensional problems by the pseudo-unsteady method, the proposed schemes require the CPU time smaller than in the case of the known TVD schemes by a factor of six.

Keywords: hyperbolic conservation laws, Lagrange-Burmann expansions, difference methods

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