The FitzHugh-Nagumo model is a reaction-diffusion equation
describing the propagation of electrical signals
in nerve axons and other biological tissues.
One of the model parameters is the ratio ε of two time scales,
which takes values between 0.001 and 0.1 in typical simulations
of nerve axons.
Based on the existence of a (singular) limit at ε=0,
it has been shown that the FitzHugh-Nagumo equation admits
a stable traveling pulse solution for sufficiently small ε>0.
In this paper we prove the existence of such a solution for ε=0.01.
We consider both circular axons and axons of infinite length.
Our method is non-perturbative and should apply
to a wide range of other parameter values.