Suppose f"(x) = N¿(h) + a,h + azh² + azh³ + -· The value of N½(h) using Richardson's extrapolation is:
Suppose f"(x) = N¿(h) + a,h + azh² + azh³ + -· The value of N½(h) using Richardson's extrapolation is:
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 f'"(x) = N,(h) + a,h + azh² + azh³ + ….
The value of N2(h) using Richardson's extrapolation is:
N2 (h)=(4N1(h/2)-N1 (h))/3 with
error of order O(h^4 )
N2 (h)=2N1 (h/2)-N1 (h) with error
of order O(h)
N2 (h)=2N1 (h/2)-N1 (h) with error
of order O(h^2)
N2 (h)=(4N1(h/2)-N1 (h))/3 with
error of order O(h^2 )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5b8d54d-590f-49c4-9ea0-bf2975ebf865%2Fec07317e-d9e4-4959-b856-d0cbfe45a5f7%2F03518hp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose f'"(x) = N,(h) + a,h + azh² + azh³ + ….
The value of N2(h) using Richardson's extrapolation is:
N2 (h)=(4N1(h/2)-N1 (h))/3 with
error of order O(h^4 )
N2 (h)=2N1 (h/2)-N1 (h) with error
of order O(h)
N2 (h)=2N1 (h/2)-N1 (h) with error
of order O(h^2)
N2 (h)=(4N1(h/2)-N1 (h))/3 with
error of order O(h^2 )
![Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the
3- point numerical differentiation scheme that will best approximate f'(0.6).
Backward difference with h=0.6
Forward difference with h=0.3
Forward difference with h=0.6
Backward difference with h=0.3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5b8d54d-590f-49c4-9ea0-bf2975ebf865%2Fec07317e-d9e4-4959-b856-d0cbfe45a5f7%2Fge0ywi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the
3- point numerical differentiation scheme that will best approximate f'(0.6).
Backward difference with h=0.6
Forward difference with h=0.3
Forward difference with h=0.6
Backward difference with h=0.3
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