The difference potentials analogous to classic Cauchy integrals were supposed in 1969 and were significantly generalized later. In the article the construction of difference potentials for linear difference scheme on the arbitrary grid of abstract points is expounded. The scheme is not restricted by any conditions besides the natural request of unique existence of the solution at arbitrary right hand side. The part of generated difference potential for solutions of difference scheme is similar to part of classic Cauchy integral for solutions of Cauchy-Riemann system, i.e. for analytical functions. The method using these difference potential for applications gives new possibilities because joins universality and algorithmicity of classic difference schemes with some dignities of classic Cauchy integral.

Mathematical problems and theory of numerical methods