Abstract
We consider numerical continuation and detection of bifurcation of solutions of large nonlinear systems, particularly those derived from discretization of partial differential equations. The basic idea is to start from a nonsingular solution and continue it with respect to a control parameter. If a bifurcation is detected between two consecutive continuation steps, we undertake a local analysis of the bifurcation scenario and stability of bifurcating solution branches. Thereafter, we switch to a chosen solution branch and continue it further. Both continuation and bifurcation analysis involve solution of large linear systems. Iterative methods and preconditioning techniques are studied for efficient solution of large linear systems and eigenvalue problems.
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