Invariantization of numerical schemes using moving frames

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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