  Flexion-based weak gravitational lensing analysis is proving to be a useful
adjunct to traditional shear-based techniques. As flexion arises from gradients
across an image, analytic and numerical techniques are required to investigate
flexion predictions for extended image/source pairs. Using the Schwarzschild
lens model, we demonstrate that the ray-bundle method for gravitational lensing
can be used to accurately recover second flexion, and is consistent with
recovery of zero first flexion. Using lens plane to source plane bundle
propagation, we find that second flexion can be recovered with an error no
worse than 1% for bundle radii smaller than {\Delta}{\theta} = 0.01 {\theta}_E
and lens plane impact pararameters greater than {\theta}_E + {\Delta}{\theta},
where {\theta}_E is the angular Einstein radius. Using source plane to lens
plane bundle propagation, we demonstrate the existence of a preferred flexion
zone. For images at radii closer to the lens than the inner boundary of this
zone, indicative of the true strong lensing regime, the flexion formalism
should be used with caution (errors greater than 5% for extended image/source
pairs). We also define a shear zone boundary, beyond which image shapes are
essentially indistinguishable from ellipses (1% error in ellipticity). While
suggestive that a traditional weak lensing analysis is satisfactory beyond this
boundary, a potentially detectable non-zero flexion signal remains.
