USE OF YU. D. SOKOLOV'S METHOD IN SOLVING DIRICHLET PROBLEM FOR POISSON'S EQUATION

摘要

The solving of Dirichlet's internal problem for-Poisson's equation by the method of potentials leads to Freehold’s linear integral equation of the-second type. The present work shows that Sokolov's method [l, 2) used for such a class of integral equations is always coinciding and reliable with respect to round-off errors.n1. Let us have in some full Gilbert space the linear operative equationnThe equation (l) will be solved by Sokolov's method, building consequent approximations according to formula wherenxo and φ are free elements of the H scope, CP is a proper element of the A operator, which corresponds to the λ1, isolated prime proper value, i.e. to the Theorem. If the single solution of equation (l) exists and the spectrum of the A operator is found in the single circle, exceptnλ1, which generally speaking, is not found in the single circle, then the sequence (2) coincides according to the standard in H before the solution of equation (l).