Solution of a problem of nonlinear potential theory by the fixed domain method

A solution is derived for a one-dimensional boundary-value problem of nonlinear potential theory with one free end with a supplementary boundary condition. The problem is solved by a variant of the fixed domain method. In each fixed domain, the problem is reduced to the corresponding nonlinear difference problem, which is solved by Newton's method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 51–56, 1986.