Continuation for nonlinear elliptic partial differential equations discretized by the multiquadric method

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