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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…

Mathematical Physics · Physics 2010-08-17 K. Parand , S. Abbasbandy , S. Kazem , A. R. Rezaei

The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…

Numerical Analysis · Mathematics 2026-04-03 Daniele Moretto , Andrea Franceschini , Massimiliano Ferronato

The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian…

Numerical Analysis · Mathematics 2024-01-01 Xiaochuan Tian , Yixuan Wu , Yanzhi Zhang

The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…

Numerical Analysis · Mathematics 2016-06-27 Wei Zhao , Martin Stoll

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

Numerical Analysis · Computer Science 2018-06-21 Zuzana Majdisova , Vaclav Skala

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Graphics · Computer Science 2018-04-19 Zuzana Majdisova , Vaclav Skala

This paper applies meshless method of lines, which uses radial basis functions (RBFs) as a spatial collocation scheme to solve the Coupled Drinfeld's-Sokolov-Wilson System. Runge-Kutta method is used for time integration of the system of…

Numerical Analysis · Mathematics 2017-03-16 Sirajul Haq , Nagina Hassan , S. I. A. Tirmizi , Muhammad Usman

A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which…

Numerical Analysis · Mathematics 2017-01-03 Francisco Bernal , Gail Gutiérrez

In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\mathbb{R}^d$. Our method…

Numerical Analysis · Mathematics 2014-04-04 Varun Shankar , Grady B. Wright , Robert M. Kirby , Aaron L. Fogelson

We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies…

Numerical Analysis · Mathematics 2025-09-19 Sage B Shaw , Zachary P Kilpatrick , Daniele Avitabile

A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…

Numerical Analysis · Mathematics 2017-01-04 Ben F McMillan

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

Numerical Analysis · Mathematics 2018-06-12 Pankaj K Mishra , Sankar K Nath , Mrinal K Sen , Gregory E Fasshauer

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…

Numerical Analysis · Mathematics 2018-06-13 Zuzana Majdisova , Vaclav Skala

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…

Numerical Analysis · Mathematics 2020-04-20 Min Zhang , Juan Cheng , Weizhang Huang , Jianxian Qiu

Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…

Numerical Analysis · Mathematics 2019-01-07 Pankaj K Mishra , Gregory E Fasshauer , Mrinal K Sen , Leevan Ling

We present and study techniques for investigating the spectra of linear differential operators on surfaces and flat domains using symmetric meshfree methods: meshfree methods that arise from finding norm-minimizing Hermite-Birkhoff…

Numerical Analysis · Mathematics 2025-06-18 Daniel R. Venn , Steven J. Ruuth

The Lane-Emden type equations are employed in the modelling of several phenomena in the areas of mathematical physics and astrophysics . In this paper a new numerical method is applied to investigate some well-known classes of Lane-Emden…

Numerical Analysis · Mathematics 2016-05-27 Kourosh Parand , Soleiman Hashemi

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…

Fluid Dynamics · Physics 2026-03-27 Damien Rigutto , Manuel Ratz , Miguel A. Mendez

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…

Computational Engineering, Finance, and Science · Computer Science 2018-06-22 Zuzana Majdisova , Vaclav Skala

Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…

Numerical Analysis · Mathematics 2026-03-13 Henry M. Broadley , Steven J. Lind , Jack R. C. King