Assume that the following table was obtained from the solution of a differential equation 0 1 2 3 4 0.0 0.368 0.541 0.448 0.293 X у 5 0.168 (a) Using linear interpolation between adjacent nodes xi, produce a continuous graph of this data on the interval 0 ≤ x ≤ 5. Use Newton's Divided Differences formula. Show the details of your work. (b) This time use quadratic interpolation to produce a continuous graph. Make a figure of (a) and (b). You can use computer programs (excel, python, gnuplot, etc.).
Assume that the following table was obtained from the solution of a differential equation 0 1 2 3 4 0.0 0.368 0.541 0.448 0.293 X у 5 0.168 (a) Using linear interpolation between adjacent nodes xi, produce a continuous graph of this data on the interval 0 ≤ x ≤ 5. Use Newton's Divided Differences formula. Show the details of your work. (b) This time use quadratic interpolation to produce a continuous graph. Make a figure of (a) and (b). You can use computer programs (excel, python, gnuplot, etc.).
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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Transcribed Image Text:Assume that the following table was obtained from the solution of a differential equation
0
(a) Using linear interpolation between adjacent nodes x₁, produce a continuous graph of this data on
the interval 0≤x≤ 5. Use Newton's Divided Differences formula. Show the details of your work.
(b) This time use quadratic interpolation to produce a continuous graph.
Make a figure of (a) and (b). You can use computer programs (excel, python, gnuplot, etc.).
Examplary figure is shown below
2
Data set and linear interpolation
4
X
у
8
10
0
1
2
3
4
0.0 0.368 0.541 0.448 0.293
12
5
0.168
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