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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.10: Partial Fractions
Problem 17E
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Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be: f (x;) – 2f (xi-1) +f(xi-2) 1) f"(x¡) = "Backward Method" (Ax)2 f (x;) – 3f (xi-1) + 3f (xi-2) – f(xi-3) (Ax)³ 2) f'(x;) = "Backward Method" f(xi+3) – 3f(x;+2) + 3f(x;+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
Transcribed Image Text:Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be: f (x;) – 2f (xi-1) +f(xi-2) 1) f"(x¡) = "Backward Method" (Ax)2 f (x;) – 3f (xi-1) + 3f (xi-2) – f(xi-3) (Ax)³ 2) f'(x;) = "Backward Method" f(xi+3) – 3f(x;+2) + 3f(x;+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
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