Solution branching - A constructive technique
Abstract
The employment of Euler-Chord and Euler-Newton continuation methods for the generation of solution branches of non-linear equilibrium problems is described. The continuation parameter is chosen to be an approximation to arclength along the solution branch. Step-size estimates along arcs composed of regular and simple limit points are derived. Convergence of Euler-Newton (Chord) stepping from simple bifurcation points is demonstrated. The problem of the approach toward a simple bifurcation point is considered and limiting approach rates determined. In both cases, the choice of approximate arclength as the continuation parameter improves convergence behavior along branches with a 'vertical' tangent at bifurcation.
- Publication:
-
New Approaches to Nonlinear Problems in Dynamics
- Pub Date:
- 1980
- Bibcode:
- 1980nanp.rept...53D
- Keywords:
-
- Branching (Mathematics);
- Equilibrium Equations;
- Nonlinear Equations;
- Banach Space;
- Chords (Geometry);
- Limits (Mathematics);
- Newton Methods;
- Step Functions;
- Physics (General)