Invariantization of numerical schemes using moving frames
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- Invariantization of numerical schemes using moving frames
- Kim, Pilwon
- Geometric integration; Invariant scheme; Lie symmetry
- Issue Date
- BIT NUMERICAL MATHEMATICS, v.47, no.3, pp.525 - 546
- 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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