Numerical methods for eigensystems: the Orr-Sommerfeld problem as an initial value problem

AbstractA recently proposed computational method for analyzing linear ordinary differential eigensystems in which a single initial value problem is used is compared with the usual methods that require more than one initial value problem the linear independence of whose solutions must be maintained. Since the new method requires only one initial value problem difficulties with parasitic error are avoided and eigenvalues for stiff systems can be obtained using standard integration schemes without resorting to techniques such as orthonormalized integration. Examples consist of a test problem with adjustable stiffness and the Orr-Sommerfeld equation for plane Poiseuille flow