Numerical Liapunov-Schmidt spectral methods for k-determined problems

We describe several generalized Liapunov-Schmidt methods in the bordered sy stems formulation for operator equations and collect information concerning classification of bifurcation functions. We present a short outline of spe ctral methods in this bifurcation context and show the convergence of the d iscrete defining equations and nondegeneracy conditions for spectral (finit e element and difference) methods to the counterparts of the original opera tor for k-determined problems. This result is then applied to a model for T uring patterns in a two component mixture. (C) 1999 Elsevier Science S.A. A ll rights reserved.