  In this paper a nonlinear coupled Schrodinger system in the presence of mixed
cubic and superlinear power laws is considered. A non standard numerical method
is developed to approximate the solutions in higher dimensional case. The idea
consists in transforming the continuous system into an algebraic quasi linear
dynamical discrete one leading to generalized semi-linear operators. Next, the
discrete algebraic system is studied for solvability, stability, convergence
and stability. At the final step, numerical examples are provided to illustrate
the efficiency of the theoretical results.
