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Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(xi) – 2f (x¡-1) + f(xi-2) (Ax)2 1) f"(x;) = "Backward Method" %3D f(xi+2) – 2f(xi+1) + f(x;) 2) f"(xi) = "Forward Method" (Ax)2 f(xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x¡) = "Forward Method"

Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(xi) – 2f (x¡-1) + f(xi-2) (Ax)2 1) f"(x;) = "Backward Method" %3D f(xi+2) – 2f(xi+1) + f(x;) 2) f"(xi) = "Forward Method" (Ax)2 f(xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x¡) = "Forward Method"

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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Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x) – 2f(xi-1) + f(x¡-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(x;+1) + f(x¡) (Ax)2 2) f"(xi) = "Forward Method" f (xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
Transcribed Image Text:Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x) – 2f(xi-1) + f(x¡-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(x;+1) + f(x¡) (Ax)2 2) f"(xi) = "Forward Method" f (xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
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