  This paper deals with an implicit Newton-like inertial dynamical system
governed by a maximally comonotone inclusion problem in a Hilbert space. Under
suitable conditions, we establish not only pointwise estimates and integral
estimates for the velocity and the value of the associated Yosida
regularization operator along the trajectory of the system, but also the weak
convergence of the trajectory to a zero of the maximally comonotone operator.
Moreover, a new inertial algorithm is developed via a time discretization of
the proposed system. Our analysis reveals that the resulting discrete algorithm
exhibits fast convergence properties matching the ones of the continuous time
counterpart. Finally, the theoretical results are illustrated by numerical
experiments.
