2. Find Solution using Newton's Divided Difference Interpolation formula
| x | f(x) |
| 2 | 0.69315 |
| 2.5 | 0.91629 |
| 3 | 1.09861 |
x = 2.7
Solution:
The value of table for `x` and `y`
| x | 2 | 2.5 | 3 |
|---|
| y | 0.6932 | 0.9163 | 1.0986 |
|---|
Numerical divided differences method to find solution
Newton's divided difference table is
| x | y | `1^(st)` order | `2^(nd)` order |
| 2 | 0.6932 | | |
| | `(0.9163-0.6932)/(2.5-2)=0.4463` | |
| 2.5 | 0.9163 | | `(0.3646-0.4463)/(3-2)=-0.0816` |
| | `(1.0986-0.9163)/(3-2.5)=0.3646` | |
| 3 | 1.0986 | | |
The value of `x` at you want to find the `f(x) : x = 2.7`
Newton's divided difference interpolation formula is
`f(x)=y_0 +(x-x_0) f[x_0, x_1]+(x-x_0)(x-x_1) f[x_0, x_1, x_2]`
`y(2.7) = 0.6932 + (2.7 -2) xx 0.4463 + (2.7 -2)(2.7 -2.5) xx -0.0816`
`y(2.7) = 0.6932 + (0.7) xx 0.4463 + (0.7)(0.2) xx -0.0816`
`y(2.7) = 0.6932 +0.3124 -0.0114`
`y(2.7) = 0.9941`
Solution of divided difference interpolation method `y(2.7) = 0.9941`
This material is intended as a summary. Use your textbook for detail explanation.
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