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 …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

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 …

A traditional criterion to calculate the numerical stability of the interpolation matrix is its
standard condition number. In this paper, it is observed that the effective condition number (κ …

In this paper we consider the problem of finding an optimal value of the shape parameter in
radial basis function interpolation. In particular, we propose the use of a leave-one-out cross …

Polynomials are used together with polyharmonic spline (PHS) radial basis functions (RBFs)
to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial …

Considering the acoustic refraction effect, an investigation of simultaneously visualizing the
temperature and velocity fields is carried out by using the combined meshfree radial basis …

In this paper, we propose a numerical method for the solution of time fractional nonlinear
sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum …

In this research, we propose a numerical scheme to solve the system of second-order
boundary value problems. In this way, we use the Local Radial Basis Function Differential …

Surrogate-assisted evolutionary algorithms have been commonly used in extremely
expensive optimization problems. However, many existing algorithms are only effectively …