High‐accuracy difference schemes for the nonlinear transfer equation
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 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.
First Published Online: 14 Oct 2010
Keywords:
High accuracy difference scheme, nonlinear transport equation, method of characteristicsHow to Cite
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Copyright (c) 2007 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2007 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.