Answered: Compute f(0.25) from the following data…

Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF at xo= -1 -1 0.5 0.55 0.6 0.65 0.7 f(x) -1 -1.375 -1.225625 -1.064 -0.880375 -0.677

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

d. Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF) at x₀= -1

Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF)
at xo= -1
-1
0.5
0.55
0.6
0.65
0.7
f(x)
-1
-1.375
-1.225625
-1.064
-0.880375
-0.677

III.
BACKWARD GREGORY – NEWTON INTERPOLATION FORMULA (BGNIF)
r(r+ 1)
f(x) = fo + rAf.1 +
2!
r(r+1)(r+ 2)
A°f3 +
r(r+ 1)(r + 2)(r + 3)
Aªf-4 +
3!
4!
Where:
x- the value of x whose f(x) is required
X, - chosen from the table
x = X, + rh
х— Хо
r =
h

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