A linearized finite-difference method for the solution of some mixed concave and convex non-linear problems

In the present work, a linearized finite-difference scheme is proposed in order to approximate the solution of some non-linear equation characterized by mixed concave and convex non-linearities. It is proved that the scheme is uniquely solvable and convergent. The resulting method is also analyzed for consistency and stability. Some numerical examples illustrating the method described in our work are given.