Construct the natural cubic spline interpolant s(x) to the function ƒ(x) = x² cos(x) — 3x = 0.2 and 2 = at the points xo = 0.1, x₁ (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x2) = 0. : 0.3. Recall that we need: =
Construct the natural cubic spline interpolant s(x) to the function ƒ(x) = x² cos(x) — 3x = 0.2 and 2 = at the points xo = 0.1, x₁ (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x2) = 0. : 0.3. Recall that we need: =
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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Question
Cubic spline
![[2]
Construct the natural cubic spline interpolant s(x) to the function
f(x) = x² cos(x) - 3x
at the points xo = 0.1, x₁ =
(i) s(x) to interpolate f(x)
(ii) s(x), s'(x) s"(x) to be continuous
(iii) s"(x) = s"(x₂) = 0.
0.2 and ₂
=
= 0.3. Recall that we need:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd47556-f3ce-4f39-818d-be563d9523c8%2Fbb661e7e-363a-4142-beb8-aeeba28f0a70%2Fvlaivkk_processed.png&w=3840&q=75)
Transcribed Image Text:[2]
Construct the natural cubic spline interpolant s(x) to the function
f(x) = x² cos(x) - 3x
at the points xo = 0.1, x₁ =
(i) s(x) to interpolate f(x)
(ii) s(x), s'(x) s"(x) to be continuous
(iii) s"(x) = s"(x₂) = 0.
0.2 and ₂
=
= 0.3. Recall that we need:
Transcribed Image Text:(a) Approximate f(0.18) and f'(0.18) using s(x) and s'(x), respectively,
and list the relative errors.
(b) Approximate ƒ'(0.2) using s'(x). Do the values ƒ'(0.2) and s'(0.2)
agree? Based on the definition of a cubic spline, should they agree?
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