Abstarct: Many problems are modeled with ordinary differential equations or partial differential equa- tions, we can transform most of them to integral or integro-differential equations with initial or boundary conditions. In order to solve these equations we require numeric methods, one of the methods of multi-variable approximation on global domains is approximation with the finite ele- ment method which takes place by meshing of the domain, this method is the baxse of many numeric methods particularly in solving partial differential equations. There is another methods known as the meshfree methods, in these approachs meshing of the domain as finite elements is not used and instead of it the approximation is implemented baxsed on a set of points which have been distributed in the region. Easier generalization to higher dimensions is one of the advantages of the meshfree methods compared to the finite element method,in this thesis we study the meshfree methods of moving least squares and interpolating moving least squares to numerically solve some integral and nonlinear integro-differential equations.