The present article considers the iterative method for the numerical solution of the Dirichlet problem for quasilinear elliptic equation. For constructing the iterative method, the difference analog of the Grin function for the Laplace operator is used.

The uniform convergence of the iterative method is proved, as well as the convergence of the solution of the difference scheme to the exact solution of the initial differential problem.

The uniform convergence of the iterative method is proved, as well as the convergence of the solution of the difference scheme to the exact solution of the initial differential problem.