A particular finite difference approximation for the first derivative of a function is -f(x+3)+9f(x+1)-8f(x;) f'(x₁) = 6h where the points are all equally spaced with a step size h. What is the order of the truncation error? Hint: use the Taylor series expansions for f(x+3) and f(x₁+₁).

A particular finite difference approximation for the first derivative of a function is -f(x+3)+9f(x+1)-8f(x;) f'(x₁) = 6h where the points are all equally spaced with a step size h. What is the order of the truncation error? Hint: use the Taylor series expansions for f(x+3) and f(x₁+₁).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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Question

A particular finite difference approximation for the first derivative of a function is
f'(x) =
-f(x+3)+9f(x₁₁)-8f(x)
6h
where the points are all equally spaced with a step size h. What is the order of the truncation error?
Hint: use the Taylor series expansions for f(x+3) and ƒ(x₁+1).

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