ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and pseudospectral methods) are based on p...

In this talk, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence t...

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashi...

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...

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The discretizes partial derivatives at scattered points using radial basis functions (RBF) as interpolants. Higher-order polynomials are appended to polyharmonic splines (PHS-RBF) and a collocation method is used derive interpolation coefficients. interpolating...

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 we present a model for the valuation, optimization, market and credit risk management of natural gas storage facilities and associated derivative contracts. A reduced form Markovian term structure model for the gas forward curve is developed and is shown to describe over 98% of the total historical variation of the fluctuations of the Henry Hub Futures curve. This approach facilit...

Abstract. In this paper, shallow water equations (SWE) are solved through a variety of meshless methods known as radial basis functions (RBF) methods. RBF based Meshless methods have gained much attention in recent years for both the mathematics as well as the engineering community. They have been extensively popularized owing to their flexibility, power and simplicity in solving partial differ...