Regularized modified α-processes for nonlinear equations with monotone operators

For a stable approximation of the solution to a nonlinear irregular equation with a monotone operator, a two-step method based on Lavrent’ev scheme and nonlinear regularized α-processes is constructed. These processes are shown to have a linear convergence rate when used to approximate the solution of a regularized equation. The error of the regularized solution is estimated, and the two-step method is shown to be order optimal in the well-posedness class of sourcewise representable solutions.