Moving least square for systems of integral equations

摘要

This paper aims at developing a meshless approximation based on the Moving Least Square (MLS), in addition to its application for solving a system of linear Fredholm integral equations of the second kind. For the MLS, nodal points are used to approximate the unknown functions. These points can be selected as regular or random from the domain under study. The method is a meshless one, and since it uses a local shape function in the vicinity of each nodal point which is chosen from the support points, it does not depend on the geometry of the domain. In this method, the unknown function is considered as a vector of functions of its kind. An error analysis has also been provided for this new method. A simple and efficient application of this method has also demonstrated through several numerical examples.