ABSTRACT
We describe numerical methods for bifurcation problems. In particular, we exploit symmetry in certain semilinear elliptic eigenvalue problems with Neumann boundary conditions for the continuation of solution curves. We show that symmetry enables us to decompose our problems into small ones, and the discretization matrix obtained via central differences associated to the Laplacian is similar to a symmetric one. Furthermore, the discrete problems preserve some basic properties on eigenvalues of the continuous problems. Sample numerical results are reported.
