A numerical solution technique based on the Chebyshev pseudospectral method is presented for solving boundary value and generalized complex eigenvalue problems which are valid over connected domains coupled through interfacial boundary conditions. As an example, the eigenvalue problem that describes the linear stability of two superposed inelastic Carreau-Yasuda fluids in plane Poiseuille flow is considered. Collocation points are formed by following two different approaches and it is shown that the accuracy of the results are highly dependent on the choice of collocation points. Therefore, in the success of pseudospectral method, a proper selection of collocation points for boundary value and eigenvalue problems is very crucial. © 2000 Elsevier Science Ltd. All rights reserved.