Numerical Methods for Bifurcation Problems: Proceedings of the Conference at the University of Dortmund, August 22–26, 1983

Front Matter....Pages 1-13
Bifurcations Arising in the Calculation of Critical Points via Homotopy Methods....Pages 15-28
Approximation of Hopf Bifurcation for Semilinear Parabolic Equations....Pages 29-41
Defining Equations for Singular Solutions and Numerical Applications....Pages 42-56
Organizing Centers for Discrete Reaction Diffusion Models....Pages 57-67
Discrete Versus Continuous Models for Dissipative Systems....Pages 68-78
“Real” and “Ghost” Bifurcation Dynamics in Difference Schemes for ODEs....Pages 79-104
The Use of Extrapolation for the solution of Bifurcation Problems....Pages 105-115
Techniques for Large Sparae Systems Arising from Continuation Methods....Pages 116-128
The Calculation of High Order Singularities in the Finite Taylor Problem....Pages 129-144
On Hopf and Subharmonic Bifurcations....Pages 145-161
Quadratically Appended Linear Models for Locating Generalized Turning Points....Pages 162-170
Hysteresis in a Model for Parasitic Infection....Pages 171-180
Continuation of Periodic Solutions in Ordinary Differential Equations — Numerical Algorithm and Application to Lorenz Model....Pages 181-194
Singular Points and their Computation....Pages 195-209
On a General Technique for Finding Directions Proceeding from Bifurcation Points....Pages 210-218
Steady State and Periodic Solution Paths: their Bifurcations and Computations....Pages 219-246
Numerical Deterkination of Bifurcation Points in Steady State and Periodic Solutions — Numerical Algorithms and Examples....Pages 247-270
Feedback Stimulated Bifurcation*....Pages 271-284
Numerical Studies of Torus Bifurcations....Pages 285-295
Numerical Treatment of Bifurcation Branches by Adaptive Condensation....Pages 296-309
Numerical Determination of Multiple Bifurcation Points....Pages 310-318
Continuation Near Symmetry-Breaking Bifurcation Points....Pages 319-334
The Numerical Bückling of a Visco-elastic Rod....Pages 335-343
Asymptotic Error Expansion for Finite Difference Schemes for Elliptic Systems Near Turning Points....Pages 344-351
Global Aspects of Newton’s Method for Nonlinear Boundary Value Problems....Pages 352-368
Finite Dimensional Approximation of Some Bifurcation Problems in Presence of Symmetries....Pages 369-384
Computation of Generalized Turning Points and Two-Point Boundary Value Problems....Pages 385-400
On Some Methods for the Computational Analysis of Manifolds....Pages 401-425
Direct Methods for The Computation of a Nonsimple Turning Point Corresponding to a Cusp....Pages 426-440
On the Axisymmeteric Buckling of Thin Spherical Shells....Pages 441-451
On the Rate of Convergence for the Approximation of Nonlinear Problems....Pages 452-458
Algorithms for Finite-Dimensional Turning Point Problems from Viewpoint to Relationships with Constrained Optimization Methods....Pages 459-479
A Continuation Algorithm with Step Control....Pages 480-494
Bifurcation near multiple eigenvalues for the flow between concentric counterrotating cylinders....Pages 495-501
The Numerical Calculation of Cusps, Bifurcation Points and Isola Formation Points in Two Parameter Problems....Pages 502-514
Mode jumping of imperfect, buckled. rectangular plates....Pages 515-524
Application of Bifurcation Theory to the Solution of Nonlinear Stability Problems in Mechanical Engineering....Pages 525-546
A Singular Multi-Grid Iteration Method for Bifurcation Problems....Pages 547-561
Regular Systems for Bifurcation Points with Underlying Symmetries....Pages 562-574
Newton Iterates for Positive Solutions of a Class of Nonlinear Eigenvalue Problems....Pages 575-584