·[²₁₁-²² Compute (a) Trapezoidal rule de using the
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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![Compute
e
dx using the
(a) Trapezoidal rule
(b) Trapezoidal rule with end corrections using the first derivative
(c) Trapezoidal rule with end corrections using the first derivative and third derivatives
(d) Gauss-Legendre quadrature
• Perform this by subdividing [-1, 1] into N e {2, 5, 10, 20, 50, 100} panels
• Plot the decay of the absolute error using the above methods.
• You may obtain the exact value of the integral upto 20 digits using wolframalpha.
• Make sure the figure has a legend and the axes are clearly marked.
• Ensure that the font size for title, axes, legend are readable.
• Submit the plots obtained, entire code and the write-up.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97c128c5-ad98-4a67-a64a-1a631e9b7f3f%2F792012f2-36c8-4c4e-8fb7-eb2edcc1bf2a%2F4ftaard_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Compute
e
dx using the
(a) Trapezoidal rule
(b) Trapezoidal rule with end corrections using the first derivative
(c) Trapezoidal rule with end corrections using the first derivative and third derivatives
(d) Gauss-Legendre quadrature
• Perform this by subdividing [-1, 1] into N e {2, 5, 10, 20, 50, 100} panels
• Plot the decay of the absolute error using the above methods.
• You may obtain the exact value of the integral upto 20 digits using wolframalpha.
• Make sure the figure has a legend and the axes are clearly marked.
• Ensure that the font size for title, axes, legend are readable.
• Submit the plots obtained, entire code and the write-up.
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