Finite Differences and Interpolation

Finite differences play a key role in the solution of differential equations and in the formulation of interpolating polynomials. The interpolation is the art of reading between the tabular values. Also the interpolation formulae are used to derive formulae for numerical differentiation and integration.


Suppose that a function y = f (x) is tabulated for the equally spaced arguments x0, x0 + h, x0 + 2 h,…, x0 + nh giving the functional values y0, y1, y2,…, yn. The constant difference between two consecutive values of x is called the interval of differencing and is denoted by h.

The operator Δ defined by

                            Δy0 = y1y0,

                            Δy1 = ...

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