Stability and local error of difference methods for the solution of the ordinary differential equation of the first order

The present paper deals with the problem of the construction of the difference formulae for the solution of the ordinary differential equation of the first order from the given characteristic polynomial, with the effect of the choice of zeros of the characteristic polunomial on the local error of the difference methods for the equation $y'=Ay,\ y(0)=1,\ A$ being a constant, and with the dependence of the error constant on the choice of zeros of the characteristic polynomial in the general case.