A Pseudo-Arclength Continuation Method for Nonlinear Eigenvalue Problems.

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in r, lambda space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords parameter dependent boundary value problems continuation algorithm singular points symmetry breaking bifurcation reaction diffusion equations.