  The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation
method with global basis functions. It is known to have exponentional
convergence for interpolation problems. We descretize nonlinear elliptic PDEs
by the MQ method. This results in modest size systems of nonlinear algebraic
equations which can be efficiently continued by standard continuation software
such as AUTO and CONTENT. Examples are given of detection of bifurcations in 1D
and 2D PDEs. These examples show high accuracy with small number of unknowns,
as compared with known results from the literature.
