Abstract
In the present paper a projection-iteration procedure for solving nonlinear operator-equations is described in abstract spaces. The method possesses a selection property by yielding only those solutions which have certain stability properties. Parameter-dependent equations and bifurcation problems are considered as well. It is shown that in the case of bifurcation near a simple eigenvalue, the method converges locally always to the "stable" solution except for initial values on a proper submanifold. Numerical results for a nonlinear boundary-value problem are given illustrating this selection character.
| Translated title of the contribution | A selective projection-iteration method and bifurcation |
|---|---|
| Original language | German |
| Pages (from-to) | 11-35 |
| Number of pages | 25 |
| Journal | Numerische Mathematik |
| Volume | 29 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 1977 |
| Externally published | Yes |