High‐accuracy difference schemes for the nonlinear transfer equation

    Agnieszka Paradzinska Info
    Piotr Matus Info
DOI: https://doi.org/10.3846/1392-6292.2007.12.469-482

Abstract

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) = 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.

First Published Online: 14 Oct 2010

Keywords:

High accuracy difference scheme, nonlinear transport equation, method of characteristics

How to Cite

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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December 31, 2007
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2007-12-31

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How to Cite

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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