in this article, we apply the multiquadric radial basis function (rbf) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the kawahara equation. the scheme is based on the crank-nicolsonformulation for space derivative. the performance of the method is shown innumerical examples.

In this paper, the development and application of radial basis function-finite difference (RBF-FD) method RBF-finite time domain (RBF-FDTD) for solving electrical transient problems in power systems that are defined by time-dependent ordinary differential equations (ODEs) partial (PDEs), respectively, presented. RBFs such as Gaussian (GA), Multiquadric (MQ), Inverse Quadric (IQ), (IMQ) used the...

In a radial basis function (RBF) network, the RBF centers and widths can be evolved by a cooperative-competitive genetic algorithm. The set of genetic strings in one generation of the algorithm represents one REP network, not a population of competing networks. This leads to moderate computation times for the algorithm as a whole. Selection operates on individual RBFs rather than on whole netwo...

The response surface methodology (RSM), which typically uses quadratic polynomials, is predominantly used for metamodeling in crashworthiness optimization because of the high computational cost of vehicle crash simulations. Research shows, however, that RSM may not be suitable for modeling highly nonlinear responses that can often be found in impact related problems, especially when using limit...

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 is intender to be a simple example illustrating some of the capabilities of Radial basis function by pruning with QLP decomposition. The applicability of the radial basis function (RBF) type function of artificial neural networks (ANNS) approach for re-estimate the Box, Traingle, Epanechnikov and Normal densities. We propose an application of QLP decomposition model to reduce to the ...

A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation ...

This paper develops some mollification formulas involving convolutions between popular radial basis function (RBF) basic functions Φ, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in Rd the convolution of | • |β and (•2 + c2)−(β+2d)/2 is the generalized multiquadric (•2 + c...

In this paper, the localized method of approximate particular solutions (LMAPS) using radial basis functions (RBFs) has been simplified and applied to near-singular elliptic problems in twoand three-dimensional spaces. The leave-one-out cross validation (LOOCV) is used in LMAPS to search for a good shape parameter of multiquadric RBF. The main advantage of the method is that a small number of n...

In this paper, axisymmetric flows over stretching surfaces in a porous medium in the presence of a magnetic field with the navier boundary condition have been considered. The governing partial differential equation (PDE) has been reduced to nonlinear ordinary differential equation (ODE) by using suitable similarity transformations. The collocation methods based on Multiquadric (MQ) Radial basis...