The author proposes an effective method of solving boundary problems for equations with partial finite differences corresponding to the two-dimensional and three-dimensional problems of mathematical physics. The essence of the method consists in finding solutions in explicit form or in the form of formulae with a small number of parameters determined from a corresponding small number of algebraic equations. For partial differential equations of the second order with constant coefficients this is attained in the two-dimensional case (24) and in the three-dimensional case (50) by means of the formulae established by the author (9) and (81) respectively.
Citation Example:Polozhii G. N. On a New Method of a Numerical Solution of Boundary Problems for Elliptical Differential Equations // Ukr. Mat. Zh. - 1960. - 12, № 3. - pp. 308 - 323.