Related papers: A Radial Basis Function (RBF)-Finite Difference (F…

In this paper, a two-sided variable-coefficient space-fractional diffusion equation with fractional Neumann boundary condition is considered. To conquer the weak singularity caused by nonlocal space-fractional differential operators, a…

The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one…

This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…

We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…

When solving partial differential equations on scattered nodes using the Radial Basis Function generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs…

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of…

This paper presented a face detection system using Radial Basis Function Neural Networks With Fixed Spread Value. Face detection is the first step in face recognition system. The purpose is to localize and extract the face region from the…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimensions. Our approach introduces an adaptive mechanism by…

In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. The applicability of RBF methods is hindered by its computational demand, that requires the solution of linear systems of…

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial…

The aim of this paper is to solve numerically, using the meshless method via radial basis functions, time-space-fractional partial differential equations of type Black-Scholes. The time-fractional partial differential equation appears in…

Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…

The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…

We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…

Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…

We mainly concerned with a decoupled fractional Laplacian wave equation in this paper. A new time-space domain radial basis function (RBF) collocation method is introduced to solve the fractional wave equation, which describes seismic wave…

This article provides techniques of raising the regularity of fractional order equations and resolves fundamental questions on the one-dimensional homogeneous boundary-value problem of skewed (double-sided) fractional diffusion advection…

In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the…