  In this work, we propose a new algorithm for finding a zero in the sum of two
monotone operators where one is assumed to be single-valued and Lipschitz
continuous. This algorithm naturally arises from a non-standard discretization
of a continuous dynamical system associated with the Douglas--Rachford
splitting algorithm. More precisely, it is obtained by performing an explicit,
rather than implicit, discretization with respect to one of the operators
involved. Each iteration of the proposed algorithm requires the evaluation of
one forward and one backward operator.
