Problem 1 (15 points) (Core Course Outcome 5)/MatlabGrader Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least third order accuracy at each data point. The data is equidistant in x with spacing h. The function input shall be ⚫y: one-dimensional column vector of y values ⚫h: scalar value of spacing h The function output shall be • d2y: column vector of the same size as y containing d²y/dx² Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different from the formulas listed there: f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³) = 60h2 56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³) 60h² −5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2) (1) f"(xi) = (2) f"(xi) = +0(h) (3) 60h2 f"(xi) -2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1) = +0(h³) (4) 60h² f"(xi) = 57f(x-5) 230f(xi-4) + 290 f (xi-3)-235 f(xi-1) +118f(xi) 60h2 +0(h³) (5) Pay special attention to the sub-indices in the formulas, since some indices are skipped! For every data point, use the most accurate formula, if Eq. (3) is the most accurate, followed by Eqs. (2) and (4), and followed by Eqs. (1) and (5). Required submission: ☐ well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 1
Problem 1 (15 points) (Core Course Outcome 5)/MatlabGrader Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least third order accuracy at each data point. The data is equidistant in x with spacing h. The function input shall be ⚫y: one-dimensional column vector of y values ⚫h: scalar value of spacing h The function output shall be • d2y: column vector of the same size as y containing d²y/dx² Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different from the formulas listed there: f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³) = 60h2 56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³) 60h² −5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2) (1) f"(xi) = (2) f"(xi) = +0(h) (3) 60h2 f"(xi) -2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1) = +0(h³) (4) 60h² f"(xi) = 57f(x-5) 230f(xi-4) + 290 f (xi-3)-235 f(xi-1) +118f(xi) 60h2 +0(h³) (5) Pay special attention to the sub-indices in the formulas, since some indices are skipped! For every data point, use the most accurate formula, if Eq. (3) is the most accurate, followed by Eqs. (2) and (4), and followed by Eqs. (1) and (5). Required submission: ☐ well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 1
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Problem 1 (15 points) (Core Course Outcome 5)/MatlabGrader
Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least
third order accuracy at each data point. The data is equidistant in x with spacing h.
The function input shall be
⚫y: one-dimensional column vector of y values
⚫h: scalar value of spacing h
The function output shall be
• d2y: column vector of the same size as y containing d²y/dx²
Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different
from the formulas listed there:
f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³)
=
60h2
56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³)
60h²
−5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2)
(1)
f"(xi)
=
(2)
f"(xi)
=
+0(h)
(3)
60h2
f"(xi)
-2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1)
=
+0(h³)
(4)
60h²
f"(xi) =
57f(x-5) 230f(xi-4) + 290 f (xi-3)-235 f(xi-1) +118f(xi)
60h2
+0(h³)
(5)
Pay special attention to the sub-indices in the formulas, since some indices are skipped! For every data point, use the most accurate
formula, if Eq. (3) is the most accurate, followed by Eqs. (2) and (4), and followed by Eqs. (1) and (5).
Required submission:
☐ well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 1
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