Numerical modeling in Chebyshev collocation methods applied to stability analysis of convection problems Original Research Article

An example of a high order method (Chebyshev collocation) applied to the study of a bifurcation problem in three dimensions is presented. The non-linear basic equations are solved by an iterative technique. The first contribution to the solution is obtained using a low-order finite difference scheme while corrective terms are obtained through collocation. The bifurcation thresholds are calculated through the perturbation equations. We study the convergence of the collocation method comparing different expansions. The polynomials and their derivatives have been evaluated a priori at the collocation points instead of using the differentiation operators on those points. This procedure simplifies the implementation.