In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …

It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Partial differential equations are a vital component of the study of mathematicalmodels in
science and engineering. There are various tools and techniques developedby the …

Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

Finite differences provided the first numerical approach that permitted large-scale
simulations in many applications areas, such as geophysical fluid dynamics. As accuracy …

This book is focused on a powerful numerical methodology for solving PDEs to high
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …

Many radial basis function (RBF) methods contain a free shape parameter that plays an
important role for the accuracy of the method. In most papers the authors end up choosing …

Radial basis function (RBF) approximation is an extremely powerful tool for representing
smooth functions in nontrivial geometries since the method is mesh-free and can be …

We provide a new way to compute and evaluate Gaussian radial basis function interpolants
in a stable way with a special focus on small values of the shape parameter, ie, for “flat” …

During the last decade, three main variations have been proposed for solving elliptic PDEs
by means of collocation with radial basis functions (RBFs). In this study, we have …