Newton Forward Interpolation

Newton Forward Interpolation:

Let the function y = f (x) take the values y0, y1, y2, ...,yn corresponding to the values x0, x1, x2, ...,xn. Where xi = x0 ih, i = 0,1,2, ...,n. Suppose it is required to evaluate f (x) for the x = x0 ph, where p is any real number.

We have for any real number p, we have defined E such that


That is;


If y = f (x) is a polynimial of nth degree, then Δn 1 and higher differences will be zero. Hence


Newton’s Forward Formula.

Eaxmple: Using Newton’s forward interpolation formula,find the area of a circle of diameter 82 metre from the given table of diameter and area of circle:


Solution: The forward difference table is as follows:

Applying Newton’s forward difference formula, we have