A simple procedure for numerically obtaining the solution of a linear, differential boundary‐value problem is presented. For annth‐order equation, the technique requires the solution ofninitial‐value problems. The solution of the boundary‐value problem is then a linear combination of these solutions. The technique has very attractive features that should make it a convenient method for studying a variety of stability problems in bounded systems. As an example of these applications, the initial stability of the inertial containment device proposed by Hirsch is examined. It is found that the particular model studied is marginally stable. The results are compared with computer simulation studies of the device.