Accuracy of difference schemes for nonlinear elliptic equations with non-restricted nonlinearity

We consider the first boundary-value problem for nonlinear elliptic equations with mixed derivatives and unrestricted nonlinearity. Difference scheme for solution of a given problem class and an iterative process implementing the scheme are constructed and studied. Rigorous study of the iterative process’ convergence is conducted. Existence and uniqueness of solution of nonlinear difference scheme approximating the original differential problem are proved. Estimates of convergence rates for difference schemes approximating nonlinear equation with non-restricted nonlinearity are obtained. These estimates are consistent with the smoothness of the sought solution.