Polynomials based methods for linear nonconstant coefficients eigenvalue problems

A method based on generalized Jacobi polynomials is proposed to solve the eigenvalue problem governing the Lyapunov stability of the mechanical equilibria of certain fluids occurring in complex circumstances. Two concrete natural convection problems of great interest from the applications point of view are numerically investigated. Fairly accurate approximations of the lower part of the spectrum are given in comparison with other numerical evaluations existing in the literature.