A leading-edge model due to McClung
is used to describe the
run-up and run-out of avalanches. The modeling process results
in a singular initial value problem which is solved
numerically using an appropriately adapted version of
the IDeC method. In Section 1 the model and
its parameters are specified. In Section
2 existence, uniqueness and smoothness
properties of the analytical solution of the problem
are discussed. In Sections 3 and
4 we describe the algorithm and technical
details of the implementation. The results of some
numerical experiments are given in Section
5.