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 …

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 …

Partial differential equations are a vital component of the study of mathematical models in
science and engineering. There are various tools and techniques developed by the …

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

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 …

Hardy's multiquadric and its related interpolators have been found to be highly efficient for
interpolating continuous, multivariate functions, as well as for the solution of partial …

The local RBF is becoming increasingly popular as an alternative to the global version that
suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of …

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 …

Radial basis functions (RBFs) have become a popular method for interpolation and solution
of partial differential equations (PDEs). Many types of RBFs used in these problems contain …

In this article, radial basis function collocation scheme is adopted for the numerical solution
of fractional partial differential equations. This method is highly demanding because of its …