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Kim, Pilwon
Nonlinear Complex Systems Lab
Research Interests
  • Complex systems, collective dynamics, nonlinear dynamical systems

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Invariantization of the Crank-Nicolson method for Burgers' equation

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Title
Invariantization of the Crank-Nicolson method for Burgers' equation
Author
Kim, Pilwon
Issue Date
2008-02
Publisher
ELSEVIER SCIENCE BV
Citation
PHYSICA D-NONLINEAR PHENOMENA, v.237, no.2, pp.243 - 254
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.
URI
https://scholarworks.unist.ac.kr/handle/201301/8942
URL
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=38549128359
DOI
10.1016/j.physd.2007.09.001
ISSN
0167-2789
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MTH_Journal Papers
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