Compound matrix method for eigenvalue problems in multiple connected domains

Abstract

An algorithm based on a compound matrix method is presented for solving difficult eigenvalue problems of n equation sets in connected domains that are coupled through ( n – 1) sets of interfacial boundary conditions, when n is an arbitrary number. As an example, a linear stability problem of n -layer plane Poiseuille flow is formulated. The resulting Orr–Sommerfeld equations form a set of stiff differential equations at high wavenumbers, which are solved accurately for various combinations of parameters.