  In this paper, we present an approximation of the matching coverage on large
bipartite graphs, for {\em local} online matching algorithms based on the sole
knowledge of the remaining degree of the nodes of the graph at hand. This
approximation is obtained by applying the Differential Equation Method to a
measure-valued process representing an alternative construction, in which the
matching and the graph are constructed simultaneously, by a uniform pairing
leading to a realization of the bipartite Configuration Model. The latter
auxiliary construction is shown to be equivalent in distribution to the
original one. It allows to drastically reduce the complexity of the problem, in
that the resulting matching coverage can be written as a simple function of the
final value of the process, and in turn, approximated
  by a simple function of the solution of a system of ODE's. By way of
simulations, we illustrate the accuracy of our estimate, and then compare the
performance of an algorithm based on the minimal residual degree of the nodes,
to the classical greedy matching.
