Continuation Near Symmetry-Breaking Bifurcation Points

Abstract

One class of examples of nonlinear boundary value problems whose discretizations in general inherit bifurcation properties from the continuous case are problems with symmetries. We analyze the behaviour of a generalized inverse iteration method for the numerical Solution of these problems near a symmetry-breaking pitchfork bifurcation point. While the computation of Symmetrie solutions does not represent any difficulties it is shown that a suitable form of the algorithm may be used to determine the bifurcating branch of non-symmetric solutions in a very stable and efficient way. The theoretical results are confirmed by numerical results for a classical example.