We discuss a leading-edge model used in the computation of the
run-out length of dry-flowing avalanches. The model has the form of a
singular initial value problem for a scalar ordinary differential
equation describing the avalanche dynamics. Existence, uniqueness
and smoothness properties of the analytical solution are shown. We also prove
the existence of a unique root of the solution.
Moreover, we present a FORTRAN 90 code for the numerical
computation of the run-out length. The code is based on a solver
for singular initial value problems which is an implementation of
the acceleration technique known as Iterated Defect Correction
based on the implicit Euler method.