Find Solution using Bessel's formula
x = 25
Finding f(2)
Solution:
The value of table for `x` and `y`
Bessel's method to find solution
`h=24-20=4`
Taking `x_0=24` then `p=(x-x_0)/h=(x-24)/4`
The difference table is
| `x` | `p=(x-24)/4` | `y` | `Deltay` | `Delta^2y` | `Delta^3y` |
| 20 | -1 | 24 | | | |
| | | 8 | | |
| 24 | 0 | 32 | | -5 | |
| | | 3 | | 7 |
| 28 | 1 | 35 | | 2 | |
| | | 5 | | |
| 32 | 2 | 40 | | | |
`x = 25`
`p = (x - x_0)/h = (25 - 24)/4 = 0.25`
`y_0=32, Delta y_0=3,Delta^2y_(-1)=-5,Delta^3y_(-1)=7`
Bessel's formula is
`y_p=(y_0+y_1)/2+(p-1/2)*Delta y_0 + (p(p-1))/(2!) * (Delta^2y_(-1)+Delta^2y_(0))/2 + ((p-1/2)p(p-1))/(3!) * Delta^3y_(-1)`
`y_(0.25) = (32+35)/2 + (0.25-1/2)*(3) + (0.25(0.25-1))/(2)*((-5+2))/2 + ((0.25-1/2)0.25(0.25-1))/(6)*(7)`
`y_(0.25)=33.5-0.75 +0.140625 +0.0546875`
`y_(0.25)=32.9453`
Solution of Bessel's interpolation is `y(25) = 32.9453`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
