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On the accuracy of invariant numerical schemes

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  • 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.
    Mathematics Subject Classification: Primary: 58J70, 35A35; Secondary: 65D30.


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