Numerical solution of eigenvalue problems using spectral techniques

Two algorithms based on spectral Chebyshev and pseudospectral Chebyshev methods are presented for solving difficult eigenvalue problems that are valid over connected domains coupled through interfacial conditions. To demonstrate the applicability of these methods, we have examined the eigenvalue problems that describe the linear stability of two superposed Newtonian and inelastic power law fluids in plane Poiseuille flow for a selected range of parameters. Both algorithms provide accurate results and the pseudospectral code appears to be more efficient in handling linear stability problems.