1. A method of performing a simulation of a subsurface hydrocarbon reservoir, the reservoir being approximated by a reservoir model having a plurality of cells, each cell having associated therewith an equation set representing a reservoir property, the method comprising: (a) determining a stability limit for each of the plurality of cells; (b) assigning each cell to one of an explicit formulation or an implicit formulation; (c) providing an initial guess to a solution for a system of equations formed using the equation set for each cell in the plurality of cells; (d) using the initial guess to solve for a solution to the system of equations using an explicit formulation for cells assigned thereto and an implicit formulation for cells assigned thereto; (e) establishing a list of unconverged cells, the unconverged cells having equation sets that have not satisfied a convergence criterion; (f) calculating a stability limit for each of the converged cells, the converged cells having equation sets that have satisfied the convergence criterion; (g) when the number of unconverged cells is greater than a predetermined amount, constructing a reduced nonlinear system with the list of unconverged cells, the reduced nonlinear system being assigned to be solved with the implicit formulation and other cells being assigned to be solved with the explicit formulation; (h) repeating parts (d), (e), (f) and (g), substituting the solved solution for the initial guess or the most recent solved solution and substituting the equation sets corresponding to the cells in the list of unconverged cells for the system of equations or equation sets from the most recent iteration, until all equation sets satisfy the convergence criterion and a stability criterion; and (i) when all equation sets satisfy the convergence criterion and the stability criterion, outputting the solved solution as a result for a timestep of a simulation of the subsurface reservoir.