We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the "first differential approximation" is invariant under the same Lie group as the original ordinary differential equation. © Czech Technical University in Prague, 2013.
Levi, D., & Winternitz, P. (2013). Lie groups and numerical solutions of differential equations: Invariant discretization versus differential approximation. Acta Polytechnica, 53(5), 438–443. https://doi.org/10.14311/AP.2013.53.0438