A meshless based method for solution of integral equations

Abstract

This article describes a numerical scheme based on the moving least squares (MLS) method for solving integral equations in one- and two-dimensional spaces. For the MLS, nodal points spread over the analyzed domain, are utilized to approximate the unknown physical quantities. The method is a meshless method, since it does not require any background interpolation or approximation cells and it dose not depend to the geometry of domain. Thus for the two-dimensional Fredholm integral equation, a non-rectangular domain can be considered. Error analysis is provided for the new method. The proposed scheme is simple and computationally attractive. Applications are demonstrated through illustrative examples. © 2009 IMACS.