A Natural cubic spline S for a function f defined on [0,2] by So (x)= 4ax + bx² + cx³ if 0
A Natural cubic spline S for a function f defined on [0,2] by So (x)= 4ax + bx² + cx³ if 0
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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![0.163182
O 0.171786
A Natural cubic spline S for a function f defined on [0,2] by
So (x) = 4ax + bx² + c x³
if 0sx<1
S (x) = d(x – 1) + e(x – 1)²- (x – 1)3 if1sxs2
Determine a, b, c, d and e such this cubic spline passes through (0;1) ; (1;0) and (2:3).
O 1. a=-2; b=0; c=1; d=1; e=3
2. a=-2; b=D0; c=-1; d31; e=3
3. a=-2; b=0; c=D1; d=-1; e=3
O 4. a=-2; b=0; c=-1; d=-1; e=3
Suppose that the values of a smooth function fis known for x= 0,0.3, 0.9, 1.2, 1.5 and 1.8. Select
the
3- point numerical differentiation scheme that will best approximatef(0.9).
Backward difference with h=0.6
III](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2546461-e59a-49f5-b7fd-6fcdc5d4ddce%2Fb46d36d7-5d71-4974-bf47-88ad84266e21%2F86wqgx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:0.163182
O 0.171786
A Natural cubic spline S for a function f defined on [0,2] by
So (x) = 4ax + bx² + c x³
if 0sx<1
S (x) = d(x – 1) + e(x – 1)²- (x – 1)3 if1sxs2
Determine a, b, c, d and e such this cubic spline passes through (0;1) ; (1;0) and (2:3).
O 1. a=-2; b=0; c=1; d=1; e=3
2. a=-2; b=D0; c=-1; d31; e=3
3. a=-2; b=0; c=D1; d=-1; e=3
O 4. a=-2; b=0; c=-1; d=-1; e=3
Suppose that the values of a smooth function fis known for x= 0,0.3, 0.9, 1.2, 1.5 and 1.8. Select
the
3- point numerical differentiation scheme that will best approximatef(0.9).
Backward difference with h=0.6
III
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