Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

Though the technique introduced by Kansa is very successful in engineering applications,
there were no proven results so far on the unsymmetric meshless collocation method for …

Promising numerical results using once and twice integrated radial basis functions have
been recently presented. In this work we investigate the integrated radial basis function …

The growing number of applications of fractional derivatives in various fields of science and
engineering indicates that there is a significant demand for better mathematical algorithms …

This paper is concerned with the development of a new compact 9-point stencil, based on
integrated-radial-basis-function (IRBF) approximations, for the discretisation of the first …

Any global or high order approximation method suffers from the Gibbs phenomenon if the
approximant has a jump discontinuity in the given domain. In this note, we present a …

A meshless procedure with a multi-quadric radial basis function is proposed for the
numerical solution of oscillatory Volterra integral equations. Integral operator of the Volterra …

This paper reports a new spectral collocation method for numerically solving two-
dimensional biharmonic boundary-value problems. The construction of the Chebyshev …

In this work, meshless methods based on a radial basis function (RBF) are applied for the
solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point …