We survey some recent developments of the application of compactly supported radial basis functions (CS-RBFs) in the context of the dual reciprocity method. Using the CSRBFs as the main tool for approximating the right hand side of a given partial differential equation, we further introduce a number of numerical techniques so that a large class of partial differential equations can be solved nu...

This paper makes two pedagogical contributions. First, we describe two macro operators for best-first search algorithms: the collapse macro where a subtree is deleted from memory and its best frontier value is stored in its root, and, the restore macro (the inverse of collapse) where the subtree is restored to its previous structure. We show that many known search algorithms can be easily descr...

We survey some recent developments of the application of compactly supported radial basis functions (CS-RBFs) in the context of the dual reciprocity method. Using the CSRBFs as the main tool for approximating the right hand side of a given partial differential equation, we further introduce a number of numerical techniques so that a large class of partial differential equations can be solved nu...

Radial basis functions (RBFs) have found important applications in areas such as signal processing, medical imaging, and neural networks since the early 1980’s. Several applications require that certain physical properties are satisfied by the interpolant, for example being divergence free in case of incompressible data. In this paper we consider a class of customized (e.g. divergence-free) RBF...

Riverbank filtration (RBF) consists of green drinking water production in many regions and is used as a pre-treatment phase. This study investigates the performance RBF Nile delta, Egypt, for climate change population growth scenarios 2030, 2040, 2050. presents new method predicting sharing riverbanks considering three cases: i) river stage controlling levels river, ii) increasing pumping, iii)...

In this article, we propose a simplified radial basis function (RBF) method with exterior fictitious sources for solving elliptic boundary value problems (BVPs). Three RBFs, including Gaussian, multiquadric (MQ), and inverse (IMQ) without the shape parameter, are adopted in study. With consideration of many outside domain, distance RBF is always greater than zero, such that can remove parameter...

This paper presents a new tool for fitting a divergence-free vector field tangent to a two dimensional orientable surface P ∈ R to samples of such a field taken at scattered sites on P . This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the me...

Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...