Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference method. The 4-th derivative of the exact solution has Maximum M = 2 in the interval [a, b]. The computer has round-off error e = 5 * 10 5. If we choose the value of h very small, the round-off error will be high, and if we choose h high, the truncation of error will be high. The optimal value of h that reduces both error kinds is O a. 0.186121 O b. 0.124467 O c. 0.104664 O d. 0.0699927
Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference method. The 4-th derivative of the exact solution has Maximum M = 2 in the interval [a, b]. The computer has round-off error e = 5 * 10 5. If we choose the value of h very small, the round-off error will be high, and if we choose h high, the truncation of error will be high. The optimal value of h that reduces both error kinds is O a. 0.186121 O b. 0.124467 O c. 0.104664 O d. 0.0699927
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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![Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference method.
The 4-th derivative of the exact solution has Maximum M = 2 in the interval [a, b]. The computer has
round-off error e = 5 * 10 5. If we choose the value of h very small, the round-off error will be high,
and if we choose h high, the truncation of error will be high. The optimal value of h that reduces both
error kinds is
O a. 0.186121
O b. 0.124467
O c. 0.104664
O d. 0.0699927](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0fc061b-41b8-4509-b5a7-afe2f0d3eba5%2F51c47b63-3ee3-4bf4-9547-a9652e666833%2Flov7tkc_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference method.
The 4-th derivative of the exact solution has Maximum M = 2 in the interval [a, b]. The computer has
round-off error e = 5 * 10 5. If we choose the value of h very small, the round-off error will be high,
and if we choose h high, the truncation of error will be high. The optimal value of h that reduces both
error kinds is
O a. 0.186121
O b. 0.124467
O c. 0.104664
O d. 0.0699927
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