Derive a finite difference approximation formula for the second derivative ƒ"(x;) using three - points X₁-1, X₁, and x₁+₁, where the spacing is such that_x; − x₁_₁ = 2h, and x₁+₁ − x₁ = h (non-uniform i+19 spacing). Hint: use the Taylor series expansions for f(x₁) and f(x₁+₁). Note the non-uniform spacing!

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Derive a finite difference approximation formula for the second derivative f"(x) using three
points x₁-1, X₁, and X₁+1, where the spacing is such that x₁ - x₁_₁ = 2h, and x₁ - x₁ = h (non-uniform
i-19
9
i-1
i+1
spacing). Hint: use the Taylor series expansions for f(x₁_₁)and f(x₁+1). Note the non-uniform
spacing!
Transcribed Image Text:Derive a finite difference approximation formula for the second derivative f"(x) using three points x₁-1, X₁, and X₁+1, where the spacing is such that x₁ - x₁_₁ = 2h, and x₁ - x₁ = h (non-uniform i-19 9 i-1 i+1 spacing). Hint: use the Taylor series expansions for f(x₁_₁)and f(x₁+1). Note the non-uniform spacing!
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