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3. Consider the integral ra = 1² €² I = e-jkz dx with the parameters a = 1, k = 4. a) Write the analytic solution to this integral.

3. Consider the integral ra = 1² €² I = e-jkz dx with the parameters a = 1, k = 4. a) Write the analytic solution to this integral.

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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pls solve all the three ques within 10-15 minutes with a explanation I'll give you multiple upvotes.
3. Consider the integral I = e¯jkr with the parameters a = 1, k = 4. a) Write the analytic solution to this integral. c) Plot the convergence of the numerically evaluated integral to the analytic solution with respect to the quadrature order N in the range of 2 to 200. For this analysis, define the error |I – | € = where I is the known analytic solution. Plot the error from both methods in loglog scale with respect to the quadrature order. d) Comment on the convergence properties of the uniform and Gaus- sian quadrature approaches. What is the answer to the question “what order of integration do you need"? How might that answer change with the problem parameters? Experiment!
Transcribed Image Text:3. Consider the integral I = e¯jkr with the parameters a = 1, k = 4. a) Write the analytic solution to this integral. c) Plot the convergence of the numerically evaluated integral to the analytic solution with respect to the quadrature order N in the range of 2 to 200. For this analysis, define the error |I – | € = where I is the known analytic solution. Plot the error from both methods in loglog scale with respect to the quadrature order. d) Comment on the convergence properties of the uniform and Gaus- sian quadrature approaches. What is the answer to the question “what order of integration do you need"? How might that answer change with the problem parameters? Experiment!
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