In this research, some numerical stratagem for constructing non-standard finite difference schemes for a classical ODE is discussed. From the practical point of view, two reliable logical methods for constructing the denominator functions for the discrete derivatives were employed and schemes constructed using the method of non-local approximation were used to implement them. The preservation of the qualitative properties of this differential equation by these schemes is also discussed. Numerical experiments were used to verify the reliability of the new finite difference schemes proposed for the logistic equation and the results obtained show that the schemes are computationally reliable.