Radial function collocation solution of partial differential equations in irregular domains

We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domains. When solving, also, for the position and shape parameters of the radial functions we obtain an adaptive, albeit non-linear, method. In this case, the resulting problem is a separable non-linear least squares one that can be efficiently solved by the Variable Projection method.