ON THE COMPUTATION OF MANIFOLDS OF FOLDPOINTS FOR PARAMETER-DEPENDENT PROBLEMS

For parameter-dependent nonlinear equations in Rn, a new augmentation method for computing submanifolds of foldpoints is presented. The underlying theory is based on a characterization, developed earlier, of foldpoints on solution manifolds of parameterized equations. The method allows for a locally convergent iterative computation of foldpoints of a certain class, for a continuation along paths of such foldpoints, and for a computation of simplicial approximations of higher-dimensional submanifolds of foldpoints of the same type.