Find Solution using Gauss Forward formula
| x | f(x) |
| 21 | 18.4708 |
| 25 | 17.8144 |
| 29 | 17.1070 |
| 33 | 16.3432 |
| 37 | 15.5154 |
x = 30
Finding f(2)
Solution:
The value of table for `x` and `y`
| x | 21 | 25 | 29 | 33 | 37 |
|---|
| y | 18.4708 | 17.8144 | 17.107 | 16.3432 | 15.5154 |
|---|
Gauss's forward method to find solution
`h=25-21=4`
Taking `x_0=29` then `p=(x-x_0)/h=(x-29)/4`
Now the central difference table is
| `x` | `p=(x-29)/4` | `y` | `Deltay` | `Delta^2y` | `Delta^3y` | `Delta^4y` |
| 21 | -2 | 18.4708 | | | | |
| | | -0.6564 | | | |
| 25 | -1 | 17.8144 | | -0.051 | | |
| | | -0.7074 | | -0.0054 | |
| 29 | 0 | 17.107 | | -0.0564 | | -0.0022 |
| | | -0.7638 | | -0.0076 | |
| 33 | 1 | 16.3432 | | -0.064 | | |
| | | -0.8278 | | | |
| 37 | 2 | 15.5154 | | | | |
`x = 30`
`p = (x - x_0)/h = (30 - 29)/4 = 0.25`
`y_0=17.107, Delta y_0=-0.7638,Delta^2y_(-1)=-0.0564,Delta^3y_(-1)=-0.0076,Delta^4y_(-2)=-0.0022`
Gauss's forward interpolation formula is
`y_p=y_0+p Delta y_0 + (p(p - 1))/(2!) * Delta^2y_(-1) + ((p + 1)p(p - 1))/(3!) * Delta^3y_(-1) + ((p + 1)p(p - 1)(p - 2))/(4!) * Delta^4y_(-2)`
`y_(0.25) = 17.107 + (0.25)(-0.7638) + ((0.25)(0.25 - 1))/(2) * (-0.0564) + ((0.25 + 1)(0.25)(0.25 - 1))/(6) * (-0.0076) + ((0.25 + 1)(0.25)(0.25 - 1)(0.25 - 2))/(24) * (-0.0022)`
`y_(0.25)=17.107 -0.1909 +0.0052875 +0.000296875 -0.0000375977`
`y_(0.25)=16.9216`
Solution of Gauss's forward interpolation is `y(30) = 16.9216`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
