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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 numerical schemes using moving frames

Cited 11 times inthomson ciCited 10 times inthomson ci
Title
Invariantization of numerical schemes using moving frames
Author
Kim, Pilwon
Keywords
Geometric integration; Invariant scheme; Lie symmetry
Issue Date
2007-09
Publisher
SPRINGER
Citation
BIT NUMERICAL MATHEMATICS, v.47, no.3, pp.525 - 546
Abstract
This paper deals with a geometric technique to construct numerical schemes for differential equations that inherit Lie symmetries. The moving frame method enables one to adjust existing numerical schemes in a geometric manner and systematically construct proper invariant versions of them. Invariantization works as an adaptive transformation on numerical solutions, improving their accuracy greatly. Error reduction in the Runge-Kutta method by invariantization is studied through several applications including a harmonic oscillator and a Hamiltonian system.
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DOI
10.1007/s10543-007-0138-8
ISSN
0006-3835
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PHY_Journal Papers
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