A NONLINEAR ADAPTATIVE MULTIRESOLUTION METHOD IN FINITE-DIFFERENCES WITH INCREMENTAL UNKNOWNS

In this article, we propose a new method well suited for the calculati on of unstable solutions of nonlinear eigenvalues problem. This method is derived from the classical Marder-Weitzner scheme (MW) which can b e seen as a nonlinear Richardson method. First we adapt to (MW) the us ual extension of the classical Linear Richardson scheme (LR) which con sists in computing the relaxation parameter in order to minimize the i terative residual in a suitable norm. This method is then generalized with the utilization of the Incremental unknowns (I.U.) inducing the m inimizing relaxation parameter in the embedded hierarchical subspaces. We obtain in this way both generalizations of the MW and the LR algor ithms. The numerical illustrations we give allowing comparisons betwee n the differents LK schemes (for linear problems) and some versions of the MW method (for nonlinear eigenvalue problems), point out tile bet ter speed of convergence of the new algorithms.