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High‐accuracy difference schemes for the nonlinear transfer equation

    Agnieszka Paradzinska Affiliation
    ; Piotr Matus Affiliation

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

Keyword : 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
Published in Issue
Dec 31, 2007
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