Some Studies Of The Lopi Multiquadrics Meshless Method

Abstract

An improvement of a new multiquadric collocation meshless method for
solving PDEs is presented. The scheme proposed here is a simple recipe for dealing
with the shape parameter of the multiquadric at different scales of the size of the grid.
Other technical improvements in the implementation of the method are described and a
framework for an h adaptive theory is established. Numerical experiments are provided
to demonstrate the utility and robustness of the proposed scheme.