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Problem 2 (15 points) (Core Course Outcomes 5 & 11)/MatlabGrader Consider the function f(x) = cos(x), where the argument is in radians, and its analytical second derivative d² = = cos(x) dx2f(x) 2. Use function defined on the interval 1 ≤ x ≤ 40 evaluated at Mk + 1 equally spaced points xi where Mk = mySecondDerivative Order 3 to calculate the error e; of the finite difference approximation of d² f/dx² at each point xi. For k = 7,8,9,..., 20, 21, plot the entry-wise 3-norm Lk of the error eż (see Exam 2) as a function of hk using a logarithmic scale for both Lk and hk. Notes for the MatlabGrader script submission: • Comment out clear or clear all in your script when submitting to MatlabGrader. • Generate and store the figure handle examFigl for the graph before doing any plotting commands, using examFig1 = figure (1); • Properly label both axis using the appropriate variable names (h, L). • Do not include the source code for any functions in your script submission. Necessary functions are provided on Matlab- Grader. Required submission: well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 2

Problem 2 (15 points) (Core Course Outcomes 5 & 11)/MatlabGrader Consider the function f(x) = cos(x), where the argument is in radians, and its analytical second derivative d² = = cos(x) dx2f(x) 2. Use function defined on the interval 1 ≤ x ≤ 40 evaluated at Mk + 1 equally spaced points xi where Mk = mySecondDerivative Order 3 to calculate the error e; of the finite difference approximation of d² f/dx² at each point xi. For k = 7,8,9,..., 20, 21, plot the entry-wise 3-norm Lk of the error eż (see Exam 2) as a function of hk using a logarithmic scale for both Lk and hk. Notes for the MatlabGrader script submission: • Comment out clear or clear all in your script when submitting to MatlabGrader. • Generate and store the figure handle examFigl for the graph before doing any plotting commands, using examFig1 = figure (1); • Properly label both axis using the appropriate variable names (h, L). • Do not include the source code for any functions in your script submission. Necessary functions are provided on Matlab- Grader. Required submission: well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 2

Advanced Engineering Mathematics
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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Problem 2 (15 points) (Core Course Outcomes 5 & 11)/MatlabGrader Consider the function f(x) = cos(x), where the argument is in radians, and its analytical second derivative d² = = cos(x) dx2f(x) 2. Use function defined on the interval 1 ≤ x ≤ 40 evaluated at Mk + 1 equally spaced points xi where Mk = mySecondDerivative Order 3 to calculate the error e; of the finite difference approximation of d² f/dx² at each point xi. For k = 7,8,9,..., 20, 21, plot the entry-wise 3-norm Lk of the error eż (see Exam 2) as a function of hk using a logarithmic scale for both Lk and hk. Notes for the MatlabGrader script submission: • Comment out clear or clear all in your script when submitting to MatlabGrader. • Generate and store the figure handle examFigl for the graph before doing any plotting commands, using examFig1 = figure (1); • Properly label both axis using the appropriate variable names (h, L). • Do not include the source code for any functions in your script submission. Necessary functions are provided on Matlab- Grader. Required submission: well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 2
Transcribed Image Text:Problem 2 (15 points) (Core Course Outcomes 5 & 11)/MatlabGrader Consider the function f(x) = cos(x), where the argument is in radians, and its analytical second derivative d² = = cos(x) dx2f(x) 2. Use function defined on the interval 1 ≤ x ≤ 40 evaluated at Mk + 1 equally spaced points xi where Mk = mySecondDerivative Order 3 to calculate the error e; of the finite difference approximation of d² f/dx² at each point xi. For k = 7,8,9,..., 20, 21, plot the entry-wise 3-norm Lk of the error eż (see Exam 2) as a function of hk using a logarithmic scale for both Lk and hk. Notes for the MatlabGrader script submission: • Comment out clear or clear all in your script when submitting to MatlabGrader. • Generate and store the figure handle examFigl for the graph before doing any plotting commands, using examFig1 = figure (1); • Properly label both axis using the appropriate variable names (h, L). • Do not include the source code for any functions in your script submission. Necessary functions are provided on Matlab- Grader. Required submission: well commented script source code submitted to Matlab Grader using the Canvas link for Exam 5 - Problem 2
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