Hydrostab: a universal code for solving hydrodynamic stability problems

The authors have developed a universal code for solving hydrodynamic stability problems.

Notice: Please cite the following paper if you use ‘hydrostab’.
Han-Yu Ye, Li-Jun Yang, and Qing-Fei Fu. Spatial instability of viscous double-layer liquid sheets. Physics of fluids 28, 102101(2016).
The authors have developed a universal code for solving hydrodynamic stability problems. The code is based on MATLAB and takes advantage of MATLAB’s support for object-oriented programming, especially its support for operator overloading. To solve a custom hydrodynamic stability problem, the user only needs to write an M-file containing descriptions of the governing equations and boundary conditions. The syntax for describing the equations closely resembles these equations themselves. Therefore this code will provide great convenience for user to investigate custom hydrodynamic stability problems. The code performs a normal mode analysis on linearized governing equations and boundary conditions, converting the stability problem into a generalized eigenvalue problem, and takes advantage of MATLAB’s powerful eigenvalue algorithms. Spatial discretization is performed by spectral collocation methods, hence offers high precision. The code supports two-dimensional problems in Cartesian coordinates. The code has been tested on MATLAB 6.5 and later versions of MATLAB.

This software relies on the 'MATLAB Differentiation Matrix Suite' developed by Weideman and Reddy. You can find that software on MATLAB Central.
For convenience, the files of the 'MATLAB Differentiation Matrix Suite' are included in this .zip file. The 'MATLAB Differentiation Matrix Suite' includes the following files:

ce0.m cerfa.m cerfb.m cheb2bc.m
cheb4c.m chebdif.m chebdifft.m chebint.m contents.m
fourdif.m fourdifft.m fourint.m herdif.m herroots.m
lagdif.m lagroots.m legroots.m matplot.m
orrsom.m poldif.m polint.m schrod.m sgrhs.m
sincdif.m sincdifft.m sineg.m

These files are developed by Weideman and Reddy, not the current author, and they are downloaded from
https://cn.mathworks.com/matlabcentral/fileexchange/29-dmsuite
in January 2016. You can search for 'MATLAB Differentiation Matrix Suite' in MATLAB Central for updated versions.