The extreme high-accuracy calculation of the 1D Poisson equation by the interpolation finite difference method (IFDM) is possible. Numerical calculation errors have conventionally been evaluated by comparison with theoretical solutions. However, it is not always possible to obtain a theoretical solution. In addition, when trying to obtain numerical values from the theoretical solution, the exact numerical value may not be obtained because of inherent difficulties, that is, a theoretical solution equal to the exact numerical solution does not hold. In this paper, we focus on an ordered structure of the error calculated by the high-order accuracy finite difference (FD) scheme. This approach clarifies that in the numerical calculation of the 1D Poisson equation, which is the most basic ordinary differential equation, the error of the numerical calculation can be evaluated without comparison with the theoretical solution. Furthermore, in the numerical calculation by the IFDM, not only the discrete solution but also the continuous approximate solution is defined by piecewise interpolation polynomials.