  In this article, we introduce and study three numerical methods for the
Dirichlet Monge Amp\`ere equation in two dimensions. The approaches consist in
considering new equivalent problems. The latter are discretized by a wide
stencil finite difference discretization and monotone schemes are obtained.
Hence, we apply the Barles-Souganidis theory to prove the convergence of the
schemes and the Damped Newtons method is used to compute the solutions of the
schemes. Finally, some numerical results are illustrated.
