what is newton forward method?

Answer 1

newtons forward interpolation formula
it can be used to find the value of a particular item in a range ie; extremes are known.

Yu = Y0 + U * delta Y0 + U*(U-1) / 2 factorial delta ^2 Y0 + U (U-1) (U-2) / 3 factorial delta ^3 Y0 +.....

where U = X-A / H
H - difference between the values of given value.
X - value to be determined
A - first value of the data

Answer 2

Newton's Forward Difference Formula
In the special case of equally spaced table entries the
divided difference formula can be expressed in terms
of these forward differences
f[x
k
, x
k+1
, ..., x
k+n
] = (1/n!h
n
)
n
f
k
Substituting in the formula for divided difference
interpolation we get
p
n
(x) = f
0
+ (1/h) f
0
(x-x
0
) + (1/2!h
2
)
2
f
0
(x-x
0
)(x-x
1
)
+ ... + (1/n!h
n
)
n
f
0
(x-x
0
)(x-x
1
) ... (x-x
n-1
)
or, for arguments starting at 0 and spaced by one
p
n
(x) = f
0
+ f
0
x + (1/2!)
2
f
0
x(x-1)
+ ... + (1/n!)
n
f
0
x(x-1) ... (x-n+1)
=
0
n
n
f
0
(
x
i
)
where (
x
i
) = x!/[i!(x-i)!]
This expression is called Newton's forward difference
formula