Numerical stability of one method of asymptotic stabilization

A problem of numerical projection onto a stable manifold in a neighborhood of a fixed point of hyperbolic type is considered. It is shown that a nonlinear iterative method of projection construction is stable with respect to errors occurring in solutions of intermediate problems. A formulation of the corresponding assertion and results of numerical simulations for solution of the problem on asymptotic stabilization over initial data for an equation of barotropic vortex type on a semisphere are presented.