The Radial Basis Function (RBF) numerical methods are widely adopted methodologies for solving Partial Differential Equations (PDEs) via collocation schemes. These approaches do not require data structures and are generally known as meshfree methods. In this research field, an important issue to be addressed is related to the accuracy of the computed solution that may suffers from instability due to the ill-conditioning of the interpolation matrices. In this talk, the RBF collocation methods will be discussed for three case studies: i) the source-type ows in porous media problems; ii) a financial application to option pricing; iii) the implicit surface reconstruction.

The Radial Basis Function (RBF) numerical methods are widely adopted methodologies for solving Partial Differential Equations (PDEs) via collocation schemes. These approaches do not require data structures and are generally known as meshfree methods. In this research field, an important issue to be addressed is related to the accuracy of the computed solution that may suffers from instability due to the ill-conditioning of the interpolation matrices. In this talk, the RBF collocation methods will be discussed for three case studies: i) the source-type flows in porous media problems; ii) a financial application to option pricing; iii) the implicit surface reconstruction.