# Newton Forward Interpolation

**Newton Forward Interpolation:
**

Let the function y = f (x) take the values y_{0}, y_{1}, y_{2}, ...,y_{n} corresponding to the values x_{0}, x_{1}, x_{2}, ...,x_{n}. Where x_{i} = x_{0} ih, i = 0,1,2, ...,n. Suppose it is required to evaluate f (x) for the x = x_{0} 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 Δ^{n 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