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Order 10 4 speedup in global linear instability analysis using matrix formation

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Fig. 1. Stencils, seeds Si, and domains of validity Qi of the individual polynomial interpolants /i(x) of a piecewise polynomial interpolation of degree q = 6 on 11 nodes  {N = 10)
Fig. 2. Grid spacing Axi = Xi+i - Xi of the non-uniform grid for the piecewise polynomial interpolation (solid line), for the Chebyshev interpolation (dotted line), and for the  uniform grid (dashed line) normalized with the uniform grid spacing AXIE, = 2/
Fig. 3. Relative error for the amplification rate of the leading eigenmode of plane  Poiseuille fiow at Re = W,a = 1 [49,501, obtained by (black) spectral collocation  using CGL and (blue) high-order finite-difference methods of order 8: STD, Fade,  DRP, S
Fig. 4 shows the eigenspectrum and pseudospectrum obtained  by the spectral collocation and finite-difference methods
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