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2. Show that when f'(x) is evaluated at x = Xị, the equation to calculate the unequally spaced data we discussed in the class, 2х — х, — х+1 +f(x¡) f'(x) = f(xi-1) x-1 – X;)(xi-1 - Xi+1) 2х — х-1 — Хi+1 (x; - Xi-1)(Xi - Xi-1) 2х — х-1 - Хi + f(xi+1)· (Xi+1 - Xi-1)(Xi+1 - x;) become the simple central difference equation, f(xi+1) – f(xi-1) f'(x¡) = 2h if the data are equally spaced with a step size h.

2. Show that when f'(x) is evaluated at x = Xị, the equation to calculate the unequally spaced data we discussed in the class, 2х — х, — х+1 +f(x¡) f'(x) = f(xi-1) x-1 – X;)(xi-1 - Xi+1) 2х — х-1 — Хi+1 (x; - Xi-1)(Xi - Xi-1) 2х — х-1 - Хi + f(xi+1)· (Xi+1 - Xi-1)(Xi+1 - x;) become the simple central difference equation, f(xi+1) – f(xi-1) f'(x¡) = 2h if the data are equally spaced with a step size h.

Advanced Engineering Mathematics
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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2. Show that when f'(x) is evaluated at x = x;, the equation to calculate the unequally spaced data we discussed in the class, 2х — х-1 — Хi+1 + f(x;); (Xi - Xi-1)(xi – Xi-1) 2х — х, — хі+1 f'(x) = f(xi-1) (xi-1 - Xi)(Xi-1 – Xi+1) 2х — х-1 — хi (Xi+1 - Xi-1)(xi+1 - Xi) + f(xi+1) become the simple central difference equation, f (xi+1) – f(xi-1) f'(x;) = 2h if the data are equally spaced with a step size h.
Transcribed Image Text:2. Show that when f'(x) is evaluated at x = x;, the equation to calculate the unequally spaced data we discussed in the class, 2х — х-1 — Хi+1 + f(x;); (Xi - Xi-1)(xi – Xi-1) 2х — х, — хі+1 f'(x) = f(xi-1) (xi-1 - Xi)(Xi-1 – Xi+1) 2х — х-1 — хi (Xi+1 - Xi-1)(xi+1 - Xi) + f(xi+1) become the simple central difference equation, f (xi+1) – f(xi-1) f'(x;) = 2h if the data are equally spaced with a step size h.
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