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Original Articles

High‐accuracy difference schemes for the nonlinear transfer equation

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Pages 469-482 | Received 16 Dec 2006, Published online: 14 Oct 2010
 

Abstract

In the present paper, for the initial boundary value problem for the non‐homogeneous nonlinear transport equation

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.

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