  In this paper, we consider a non-local (in time) two-phase flow model. The
non-locality is introduced through the wettability alteration induced dynamic
capillary pressure function. We present a monotone fixed-point iterative
linearization scheme for the resulting non-standard model. The scheme treats
the dynamic capillary pressure functions semi-implicitly and introduces an
$L$-scheme type \cite{List2016, Radu2015} stabilization term in the pressure as
well as the transport equations. We prove the convergence of the proposed
scheme theoretically under physically acceptable assumptions and verify the
theoretical analysis with numerical simulations. The scheme is implemented and
tested for a variety of reservoir heterogeneity in addition to the dynamic
change of the capillary pressure function. The proposed scheme satisfies the
predefined stopping criterion within a few numbers of iterations. We also
compared the performance of the proposed scheme against the iterative IMplicit
Pressure Explicit Saturation scheme
