Invariantization of the Crank-Nicolson method for Burgers’ equation |
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Authors: | Pilwon Kim |
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Institution: | Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA |
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Abstract: | In this article, a geometric technique to construct numerical schemes for partial differential equations (PDEs) that inherit Lie symmetries is proposed. The moving frame method enables one to adjust the numerical schemes in a geometric manner and systematically construct proper invariant versions of them. To illustrate the method, we study invariantization of the Crank-Nicolson scheme for Burgers’ equation. With careful choice of normalization equations, the invariantized schemes are shown to surpass the standard scheme, successfully removing numerical oscillation around sharp transition layers. |
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Keywords: | Lie symmetry Burgers&rsquo equation Invariant schemes Moving frames |
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