Numerical Liapunov—Schmidt spectral methods for k-determined problems Original Research Article

We describe several generalized Liapunov—Schmidt methods in the bordered systems formulation for operator equations and collect information concerning classification of bifurcation functions. We present a short outline of spectral methods in this bifurcation context and show the convergence of the discrete defining equations and nondegeneracy conditions for spectral (finite element and difference) methods to the counterparts of the original operator for k-determined problems. This result is then applied to a model for Turing patterns in a two component mixture.