In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1){ y′(t) = f(t, y(t), y(t− τ(t, y(t))), y′(t− σ(t, y(t)))), t1 ≤ t ≤ tf , y(t) = φ(t), t ≤ t1, where f : [t1, tf ] × R × R × R → R is a smooth function, τ(t, y(t)) and σ(t, y(t)) are continuous functions on [t1, tf ]×R such that t−τ(t, y(t)) < tf and t− σ(...

In this note a local thinning of the data locations is proposed, in order to construct a least squares multiquadric approximant stable and close to the multiquadric interpolant

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.

Promising numerical results using once and twice integrated radial basis functions have been recently presented. In this work we investigate the integrated radial basis function (IRBF) concept in greater detail, connect to the existing RBF theory, and make conjectures about the properties of IRBF approximation methods. The IRBF methods are used to solve PDEs. c © 2006 Elsevier Science Ltd. All ...

A computational algorithm based on the multiquadric, which is a continuously diierentiable radial basis function, is devised to solve the shallow-water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any diierence scheme. The method does not requ...

Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...

Radial basis function methods for interpolation can be interpreted as roughness-minimizing splines. Although this relationship has already been established for radial basis functions of the form g(r) = r and g(r) = r log(r), it is extended here to include a much larger class of functions. This class includes the multiquadric g(r) = (r 2 + c 2) 1=2 and inverse multiquadric g(r) = (r 2 + c 2) ?1=...

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation, especially for solving the differential equations numerically. The classical method is the divided difference method. However, it has been shown strongly unstable in practice. Actually, it can only be used to simulate the lower order derivatives in applicat...

In many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. Since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, GIS-based modeling approach was utilized to zoning PM2.5 dispersion over Tehran, du...

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.