EigTool Airy Demo

Our "Airy operator" is an operator acting on functions of x defined on [-1,1] according to the formula where epsilon is a small parameter. The spectrum of this operator is an unbounded discrete set contained in the half-strip Re z < 0, -1 < Im z < 1. The pseudospectra approximately fill the whole strip. The pseudospectra of this operator were first considered by Reddy, Schmid and Henningson as a model of the more complicated Orr-Sommerfeld problem [1]. Our M-file is based on a Chebyshev collocation spectral discretization with epsilon = 4e-3.

[1]: S. C. Reddy, P. J. Schmidt and D. S. Henningson, "Pseudospectra of the Orr-Sommerfeld operator", SIAM J. Appl. Math. 53(1), pp. 15-47, 1993.

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