There exist several discretization techniques for the numerical solution of partial differential
equations. In addition to classical finite difference, finite element and finite volume …

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 …

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 recent years, consistent spatial discretization schemes for meshfree particle methods to
numerically simulate incompressible flow have been studied by many researchers. This …

Meshfree discretizations of state-based peridynamic models are attractive due to their ability
to naturally describe fracture of general materials. However, two factors conspire to prevent …

In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM)
approach to discretize PDEs defined on manifolds. Derivative approximations for the same …

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation
based on numerical differentiation stencils obtained with the help of radial basis functions …

A Lagrangian meshless method is introduced for numerical simulation of flows of
incompressible fluids with free surface. Poisson Pressure Equation (PPE) formulation of …

In this follow up paper to our previous study in Bayona et al.(2011)[2], we present a new
technique to compute the solution of PDEs with the multiquadric based RBF finite difference …

We introduce in this article a unified algorithm which allows the selection of collocation
stencils, based on the visibility criterion, for convex, concave, and singular problems solved …