In this paper we use radial basis functions to solve multivariable integral equations. We use collocation Method for implementation. Numerical experiments show the accuracy of the Method.

In this paper, a computational technique is presented based on the natural element Method (NEM) for large plastic deformation simulation of the metal forming problems. NEM is a numerical technique in the field of computational mechanics and can be considered as a Meshless Method. The selected process is backward extrusion for circular shape hollow components from round billets. The punch stroke value is divided into sub-steps, whereas a new set of nodes become active at the end of each sub-step of deformation. Solutions are obtained for different area reductions under friction condition. Hollman-Ludwik law is selected to explain the material behavior after the yielding point. The experiments are carried out with fully annealed commercial aluminum alloy billets at room temperature, using various punch sizes. A set of die and punches are designed and constructed for experimental works. The validity of the proposed Method is verified by comparing the results from deformed geometry, contours of equivalent strain and forming loads with those obtained from finite element simulation and experimental measurements. It is concluded that the results obtained by NEM are in good agreement with those from FEM and experiments and therefore, the Meshless natural element Method is capable of handling large plastic deformation.

The objective of this research is to study the ability of a Meshless Method, called finite point Method, in solving incompressible fluid flow problems using two stabilization schemes. The main goal of Meshless Methods is to reduce or remove the cost of grid generation. This issue is implemented using the satisfaction of governing differential equations on a regular or irregular set of nodes by interpolation functions, based on special least-squares approximations. In this research, the finite point Method is used to solve the Stokes and the Navier-Stokes equations by employing two different stabilization schemes. In addition, the effects of least-squares approximations are studied

This paper goals to expand a Meshless Method using the collocated discrete least squares Meshless (CDLSM) approach for mathematical modeling of a category of time fractional diffusion-wave equation (TFDWE). First, moving least squares (MLS) Method used to construct the shape function is brie y described. Then, using the shape function generated by the least squares Method, the discrete shape of the TFDWE is received in the strong form. Two-dimensional test problems with different nodes and collocations distributions are studied to validate and look at the accuracy and performance of proposed Method.