A method is given for the construction of finite-difference approximation to ordinary linear differential equations, based on the assumption that the desired solution can be adequately represented by a certain interpolation polynomial. The method is explained and exemplified in Section 1. A difference approximation to an nth order ordinary linear differential equation is derived in Section 2, and in Section 3 an estimate is obtained for the truncation error in this equation by showing how it depends on the truncation errors in certain simpler finite-difference formulae which depend on the order but not on the coefficients in the differential equation. The truncation errors in these simpler formulae can be estimated by standard methods. In Section 4 is given a possible numerical procedure for calculating the difference equation together with a summary of numerical results.