Convergence Order Estimates of Meshless Collocation Methods Using Radial Basis Functions

Introduction We will treat systems of linear equations, each of the form Lu = f on\Omega ; (1.1) where\Omega is a domain in IR d and L is a linear operator, acting on complex valued functions on \Omega\Gamma The function f is given ("data") and each equation should have a nonempty space of solutions. 2 1. Introduction 1.1 Collocation Method for Single Equations Collocation is a well-known method to approximate the solution of equations of the form (1.1). The idea is to approximate the requested solution u by a function s u = n X j=1 \Phi j ff j 2 span f\Phi j g j=1;:::;n ; (1.1.1) where the \Phi j :\Omega ! C are ce