Using the following finite difference methods to estimate the first derivative of the function f(x) = Over the range 0 < x < 2 with step size h = 0.5. Then compare your numerical approximations from each method with the analytical solution by computing the relative error at each value of x. = e-* cos 2tx Forward difference, 0(h) b. Backward difference, 0(h) Central difference, 0(h²) а. С. d. Build a table of relative errors to check the accuracy of your solutions against the analytical solution.
Using the following finite difference methods to estimate the first derivative of the function f(x) = Over the range 0 < x < 2 with step size h = 0.5. Then compare your numerical approximations from each method with the analytical solution by computing the relative error at each value of x. = e-* cos 2tx Forward difference, 0(h) b. Backward difference, 0(h) Central difference, 0(h²) а. С. d. Build a table of relative errors to check the accuracy of your solutions against the analytical solution.
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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![Using the following finite difference methods to estimate the first derivative of the function
\[ f(x) = e^{-x} \cos 2\pi x \]
Over the range \( 0 \leq x \leq 2 \) with step size \( h = 0.5 \). Then compare your numerical approximations from each method with the analytical solution by computing the relative error at each value of \( x \).
a. Forward difference, \( O(h) \)
b. Backward difference, \( O(h) \)
c. Central difference, \( O(h^2) \)
d. Build a table of relative errors to check the accuracy of your solutions against the analytical solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79826512-1148-4736-b4a7-6e7f4ec13f28%2Ff26be901-1f58-4f74-b013-d2d7a3b6d51f%2Ftchmwg_processed.png&w=3840&q=75)
Transcribed Image Text:Using the following finite difference methods to estimate the first derivative of the function
\[ f(x) = e^{-x} \cos 2\pi x \]
Over the range \( 0 \leq x \leq 2 \) with step size \( h = 0.5 \). Then compare your numerical approximations from each method with the analytical solution by computing the relative error at each value of \( x \).
a. Forward difference, \( O(h) \)
b. Backward difference, \( O(h) \)
c. Central difference, \( O(h^2) \)
d. Build a table of relative errors to check the accuracy of your solutions against the analytical solution.
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