This paper presents a summary of various localized collocation schemes and their
engineering applications. The basic concepts of localized collocation methods (LCMs) are …

The localized method of fundamental solutions (LMFS) is an efficient meshless collocation
method that combines the concept of localization and the method of fundamental solutions …

This paper proposes an efficient localized meshless technique for approximating the
viscoelastic wave model. This model is a significant methodology to explain wave …

A radial basis collocation method, to solve parabolic and hyperbolic equations, based on the
local space–time domain formulation is developed and presented in this paper. The method …

In this paper we present a localized meshless method using radial basis functions (RBFs) for
solving up to six dimensional problems. To improve the difficulty of selecting a shape …

Localized collocation methods based on radial basis functions (RBFs) for elliptic problems
appear to be nonrobust in the presence of Neumann boundary conditions. In this paper, we …

In this paper, three kinds of explicit local meshless methods are compared: the local method
of approximate particular solutions (LMAPS), the local direct radial basis function collocation …

Standard radial basis functions (RBFs) offer exponential convergence, however, the method
is suffered from the large condition numbers due to their 'nonlocal'approximation. The …

This paper adopts an efficient localized meshless technique for computing the solution of the
nonlinear sinh-Gordon equation (NShGE). The NShGE is one useful description for many …

Meshless methods based on collocation with radial basis functions (RBFs) are investigated
in detail in this paper. Both globally supported and compactly supported radial basis …