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Monotone high-accuracy compact running scheme for quasi-linear hyperbolic equations

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Abstract

The monotone homogeneous bicompact difference scheme earlier proposed by the authors for the linear transport equation is generalized to the case of quasi-linear hyperbolic equations. The generalized scheme is of the fourth order of approximation in the spatial coordinates on a compact stencil and has the first order of approximation in time. The scheme is conservative, absolutely stable, monotone over a wide range of local Courant number values and can be solved by explicit formulas of the running calculation. A quasi-monotone three-stage scheme, which has the third-order approximation in time for smooth solutions, is constructed on the basis of the scheme with a first-order time approximation. Numerical results are presented demonstrating the accuracy of the proposed schemes and their monotonicity in the solution of test problems for the quasi-linear Hopf equation.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    B. V. Rogov

  2. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    M. N. Mikhailovskaya

Authors
  1. B. V. Rogov
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  2. M. N. Mikhailovskaya
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Correspondence to B. V. Rogov.

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Original Russian Text © B.V. Rogov, M.N. Mikhailovskaya, 2012, published in Matematicheskoe Modelirovanie, 2011, Vol. 23, No. 12, pp. 65–78.

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Rogov, B.V., Mikhailovskaya, M.N. Monotone high-accuracy compact running scheme for quasi-linear hyperbolic equations. Math Models Comput Simul 4, 375–384 (2012). https://doi.org/10.1134/S2070048212040060

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