Chebyshev-$$\tau$$ method for certain generalized eigenvalue problems occurring in hydrodynamics: a concise survey

Abstract The aim of this survey is to give a concise but technical and, as much possible, comprehensive introduction the resolution certain eigenvalue problems occurring in research field hydrodynamics via Chebyshev - $$\tau$$ τ method. While many details on construction mathematical models (for which we will refer notable and well-known references reported by Chandrasekhar (Hydrodynamic hydromagnetic stability, Dover, London, 1981); Straughan (The energy method, nonlinear convection, Springer, New York, 2004); Nield Bejan (Convection porous media, 2017)) not be given, attention paid practical theoretical aspects discretization continuum problem. polynomials employed expand solutions differential problem end up with discrete Finally, MATLAB codes for considered are shown detail available GitHub .