Some researchers have presented the application of radial basis function approximation to the evaluation of option contracts. In a previous study, the authors described the evaluation of Asian options by using radial basis function approximation. The numerical results indicated that the computational accuracy depended on the radial basis function and the reciprocal multi-quadric function was be...

In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...

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...

Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject certain conditions. This article introduces a novel approach for solving BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation i...

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...

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...