  In this paper, we investigate the energy problem in general relativity using
approximate Lie symmetry methods for differential equations. This procedure is
applied to Bardeen model (the regular black hole solution). Here we are forced
to evaluate the third-order approximate symmetries of the orbital and geodesic
equations. It is shown that energy must be re-scaled by some factor in the
third-order approximation. We discuss the insights of this re-scaling factor.
