using Matlab How to plot eigenfunction and perturbed argument of an Orr-Sommerfeld equation

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%How to plot normalized eigenfunction and its argument of an orr sommerfeld equation also the its epsilon pseudospectra plot .%

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Nipun
Nipun le 12 Juin 2024
Hi Kavitha,
I understand that you want to plot the normalized eigenfunction and its argument for the Orr-Sommerfeld equation, as well as its epsilon pseudospectra. Here's a basic approach using MATLAB:
1. Solve the Orr-Sommerfeld equation:
  • Use appropriate boundary conditions and discretization to solve for eigenvalues and eigenfunctions.
2. Normalize the eigenfunction:
  • Normalize the eigenfunction by dividing by its maximum value.
3. Plot the normalized eigenfunction:
  • Plot the real and imaginary parts against the argument.
4. Compute and plot epsilon pseudospectra:
  • Use the "eig" function and numerical techniques to compute and visualize the pseudospectra.
Refer to the following MathWorks documentation for more information on:
  1. Eigenvalues and Eigenvectors in MATLAB: https://www.mathworks.com/help/matlab/ref/eig.html
  2. Plotting 2D and 3D data in MATLAB: https://www.mathworks.com/help/matlab/ref/plot.html
  3. Pseudospectrum using eigenvector method in MATLAB: https://www.mathworks.com/help/signal/ref/peig.html
Hope this helps.
Regards,
Nipun

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