One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don't satisfy the Kronecker Delta property, so in this method it's not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called IN-SANE, and the results are presented and compared with the analytical solutions.

In this paper, we present an algorithm for approximating numerical solution of singularly perturbed boundary value problems by means of homotopy analysis and tau Bernestein polynomial method. The method is tested for several problems and the results demonstrate reliability and efficiency of the method.