Newton Forward Interpolation

Newton Forward Interpolation:

Let the function y = f (x) take the values y₀, y₁, y₂, ...,y_n corresponding to the values x₀, x₁, x₂, ...,x_n. Where x_i = 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 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