Department of Mathematics, The John Paul II Catholic University of Lublin, Al. Raclawickie 14, Lublin, 20–950, Poland ; Institute of Mathematics, NAS of Belarus, Surganov St.11, Minsk, 220072, Belarus
In the present paper, for the initial boundary value problem for the non‐homogeneous nonlinear transport equationthe basic principles for constructing difference schemes of any order of accuracy O(#GTM), M ≥ 1, on characteristic grids with the minimal stencil were introduced. To construct a difference scheme the Steklov averaging idea for the right‐hand sidewas used. The case of f(u) = λu2was investigated in detail. A strict analysis of the order of approximation, stability, and convergence in nonlinear case was made. The performed numerical experiments justify theoretical results.
Paradzinska, A., & Matus, P. (2007). High‐accuracy difference schemes for the nonlinear transfer equation. Mathematical Modelling and Analysis, 12(4), 469-482. https://doi.org/10.3846/1392-6292.2007.12.469-482
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the basic principles for constructing difference schemes of any order of accuracy O(#GTM), M ≥ 1, on characteristic grids with the minimal stencil were introduced. To construct a difference scheme the Steklov averaging idea for the right‐hand side
was used. The case of f(u) = λu2 was investigated in detail. A strict analysis of the order of approximation, stability, and convergence in nonlinear case was made. The performed numerical experiments justify theoretical results.