A numerical study of a non-instability due to a three-dimensional disturbance in a plane parallel flow

The solution of the differential equation governing the evolution of a localized point-centered three-dimensional disturbance in a plane parallel flow is presented. A localized bust at a finite time can be produced for certain values of the coefficients which can be determined analytically. The study was made numerically using an extension of the finite-element method to parabolic operators in space-time. The solution is obtained in the complex field by solving nonlinear systems of equations using a functional iteration method. The results are compared with results already obtained with the finite-difference method in a similar formulation of the same problem.