Invariant variational schemes for ordinary differential equations

We propose a novel algorithmic method for constructing invariant variational schemes of systems ordinary differential equations that are the Euler–Lagrange principle. The is based on invariantization standard, noninvariant discrete Lagrangian functionals using equivariant moving frames. given by corresponding invariantized functionals. showcase this general preserve and divergence symmetries associated continuous Lagrangians. Noether's theorem automatically implies resulting exactly conservative. Numerical simulations carried out show these outperform standard numerical discretizations.