We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non uniform grids and mesh adaptation. We focus o...

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified...

Wire coating is a commercial method to insulate wires for mechanical intensity and environmental protection. In this experimental study, the technique of computational intelligence used nonlinear wire analysis by soaking in Oldroyd 8-constant fluid under constant pressure gradient with help feed forward artificial neural networks (ANNs). The system partial differential equations generated proce...

Green functions of the biharmonic operator, in one and two dimensions, are used for minimum curvature interpolation of irregularly spaced data points. The interpolating curve (or surface) is a linear combination of Green functions centered at each data point. The amplitudes of the Green functions are found by solving a linear system of equations. In one (or two) dimensions this technique is equ...

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non-uniform grids and mesh adaptation. We focus o...

In this paper, the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions (RBFs). The RBF multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem. The...

The number of high resolution space imageries, in the civilian market is growing fast.This images have great interest in the photogrammetric and remote sensing communities. The problem with this images for many users, at the present time is the lack of sensor calibration information and precise ephemeris data. Consequently it is not possible to apply the precise mathematical models such as orbi...

Recently, some methods of automated generation of schematic map are proposed. However, no specific method is given for expansion of congested area on a map in the process of schematization. In fact, it is a key to produce a schematic map with great clarity. For instance, for a line network map, if there are many lines in a small area on a map, although the shape of these lines is simplified by ...

Abstract Let $$H\subset {\mathbb {Z}}^d$$ H ⊂ Z d be a half-space lattice, defined either relative to fixed coordinate (e.g. $$H = {Z}}^{d-1}\!\times \!{\mathbb {Z}}_+$$ = - <mml:...