divided attack. In a recent paper, Miesen and Boersma [3] show that such a numerical solution offers the possibility This paper describes a Chebyshev collocation method for solving the eigenvalue problem that governs the stability of parallel two-to compare the results of a coupled description of the phase flow. The method is based on the expansion of the eigenfuncproblem, in which the equations of motion for the gas and tions in terms of Chebyshev polynomials, point collocation, and the liquid are solved simultaneously, with those of the the subsequent solution of the resulting generalized eigenvalue divided attack. In the present paper, we consider the gasproblem with the QZ-algorithm. We concentrate on the question liquid stability problem from a computational rather than how to handle difficulties that arise when these ''standard'' techniques are applied to the stability problem of a thin film of liquid a physical point of view; i.e., we discuss the technique for that is sheared by a gas. After discussing this specific problem in solving the gas-liquid stability problem. Emphasis is on detail, it is argued that the method of solution can readily be applied the difficulties that are encountered when a Chebyshev to other two-phase flow configurations as well. แฎ 1997 Academic Press collocation technique is applied to the specific problem of a thin film of liquid that is sheared by a gas. After discussing these difficulties in detail and presenting some illustrating 191