Suppose f"(x) = N¿(h) + a,h + azh² + azh³ + -· The value of N½(h) using Richardson's extrapolation is:

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Chapter2: Second-order Linear Odes
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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 )
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
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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