This paper presents element-free Galerkin (EFG) method as a computational technique that can effectively avoid the disadvantage of mesh entanglement. The present method is used to analyze the static defelection of beams. The moving least squares (MLS) approximation has been used for constructing the shape function based on a set of nodes arbitrarily distributed in the analysis domain.

In this paper, we propose an efficient implementation of the ChebyshevGalerkin method for  rst order Volterra and Fredholm integro-differentialequations of the second kind. Some numerical examples are presented toshow the accuracy of the method.

In this paper, first, the von Karman nonlinear theory of plate is used to present the differential equations of large deformation of thin plates in terms of the in-plane forces and out-of-plane displacement and moment sum. Then, the Galerkin integrated formulation of problem is presented. The independent variable of this equation includes the displacement u, v, w and the moment sum M. As a basic step of the Galerkin method all variables are independent in terms of the basic functions which are given in area coordinate system and the generalized coordinates. The integrated equations for each problem are solved by Newton-Raphson to drive the generalized coordinates. Several examples are solved including isocel and right-angled triangular plates under uniform distributed load and compared with results obtained by other researchers.

In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L2, L ¥ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigated.

In this paper, the classic Galergin method for solving integral equations of the second kind is extended to fuzzy Galerkin method. Moreover, the error analysis, particularly, error estimate, stability and convergence of the extended method are studied.

The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L2-norm of the error as a function of the size of the control volumes is presented for different cases; and the rate of convergence of the method is established. The results of this study show that the proposed method is applicable in solving a variety of non-isothermal fluid flow problems.

A truly meshless local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the Heaviside function. The moving least squares (MLS) are chosen to construct the shape functions, for the MLPG method. The penalty approximation is used to impose essential boundary condition. Several numerical examples are included to demonstrate that the present method is very promising for solving the elastic problems.

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution of algebraic equations.