An analysis of a difference scheme approximating a third boundary-value problem for a second-order nonlinear differential equation (Q1975102)

The paper deals with a third boundary value problem for a nonlinear equation with unbounded nonlinearity on generalized solutions. This new direction in the theory of finite differences that is connected with the construction of difference schemes for differential equations with generalized solutions has been intensively developed. A difference scheme for solving this problem and an iterative algorithm that implements it are studied in the present work. The convergence of the iterative process is proved, and a priori estimates of the convergence rate are obtained.