On the accuracy of invariant numerical schemes

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Communications on Pure and Applied Analysis, volume 10, pages 761-783 (issn: 1534-0392, eissn: 1553-5258,

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Authors: Chhay, Marx; Hamdouni, Aziz;

doi: 10.3934/cpaa.2011.10.761

On the accuracy of invariant numerical schemes

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Abstract

In this paper we present a method of construction of invariant numerical schemes for partial differential equations. The resulting schemes preserve the Lie-symmetry group of the continuous equation and they are at least as accurate as the original scheme. The improvement of the numerical properties thanks to the Lie-symmetry preservation is illustrated on the example of the Burgers equation.

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