Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations

EJ Kansa, YC Hon - Computers & Mathematics with applications, 2000 - Elsevier
Madych and Nelson [1] proved multiquadric (MQ) mesh-independent radial basis functions
(RBFs) enjoy exponential convergence. The primary disadvantage of the MQ scheme is that …

A numerical study of some radial basis function based solution methods for elliptic PDEs

E Larsson, B Fornberg - Computers & Mathematics with Applications, 2003 - Elsevier
During the last decade, three main variations have been proposed for solving elliptic PDEs
by means of collocation with radial basis functions (RBFs). In this study, we have …

Exponential convergence and H‐c multiquadric collocation method for partial differential equations

AHD Cheng, MA Golberg, EJ Kansa… - Numerical Methods for …, 2003 - Wiley Online Library
The radial basis function (RBF) collocation method uses global shape functions to
interpolate and collocate the approximate solution of PDEs. It is a truly meshless method as …

[HTML][HTML] Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions

M Dehghan, A Shokri - Journal of computational and Applied Mathematics, 2009 - Elsevier
The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. In this
paper, we propose a numerical scheme to solve the one-dimensional nonlinear Klein …

On unsymmetric collocation by radial basis functions

YC Hon, R Schaback - Applied Mathematics and Computation, 2001 - Elsevier
Solving partial differential equations by collocation with radial basis functions can be
efficiently done by a technique first proposed by Kansa in 1990. It rewrites the problem as a …

A numerical method for solving the hyperbolic telegraph equation

M Dehghan, A Shokri - Numerical Methods for Partial …, 2008 - Wiley Online Library
Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation
in modelling reaction diffusion for such branches of sciences. In this article, we propose a …

A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates

AJM Ferreira - Composite structures, 2003 - Elsevier
The multiquadric radial basis functions (MQ) method is a recent mesh-free collocation
method with global basis functions. The MQ method for the solution of partial differential …

[HTML][HTML] Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method

AJM Ferreira, CMC Roque, P Martins - Composites Part B: Engineering, 2003 - Elsevier
In the present study the third-order theory of Reddy for composite laminated plates is
discretized using a new type of meshless method, a finite point based on the multiquadric …

Multiquadric and its shape parameter—a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation

AHD Cheng - Engineering analysis with boundary elements, 2012 - Elsevier
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 …

Analysis of composite plates using a layerwise theory and multiquadrics discretization

AJM Ferreira - Mechanics of Advanced Materials and Structures, 2005 - Taylor & Francis
A layerwise shear deformation theory for composite laminated plates is discretized using
multiquadrics. This new type of meshless method considers radial basis functions as the …