The method of consistent approximation for solving non-linear operator equations

Abstract

A NEW REGULAIZATION method is proposed for the approximate solution of non-linear equations. The method is based on the well-known idea of the construction of a compact set. As regularization parameter a mesh step compulsorily consistent with the error of the initial data is used. The method guarantees uniform convergence to the exact solution of the class in the one-dimensional and two-dimensional cases.