On two methods of approximate projection onto a stable manifold

Methods of projection onto stable invariant manifolds are important for numerical stabilization in the case when boundary conditions for the solutions of nonlinear partial differential equations are used. This paper describes two different ways of projection (the zero-approximation method and the method of linearization); in the nonlinear case, these methods differ by the directions of displacements. Some numerical experiments of stabilizing the solution to the Chafee-Infante equation are discussed and analyzed for both these methods.