In this paper we present a method based on using exponential basis functions (EBFs) to solve well-known two-dimensional time dependent engineering problems such as elasto-dynamic ones. The formulation has much in common with those in three dimensional problems while time is taken as the third axis. The solution is first approximated by a summation of EBFs and then completed by satisfying the ti...

This paper proves convergence of variations of the unsymmetric kernel-based collocation method introduced by E. Kansa in 1986. Since then, this method has been very successfully used in many applications, though it may theoretically fail in special situations, and though it had no error bound or convergence proof up to now. Thus it is necessary to add assumptions or to make modifications. Our m...

The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the ...

Ground water pollution is a serious environmental problem that may damage human health, destroy the ecosystem and cause water shortage. In all situations, we need tool to predict the pollutant distribution in ground water. The only tool that we can use is mathematical modeling. Recently, very intensive efforts have been devoted to develop meshless or element free methods that eliminate the need...

In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collocation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless collocation to approximate Lyapunov functions for dynamical systems.

We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domain...

The Burgers’ equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two d...

Burgers’ equations is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation numerically using the finite difference and collocation methods. After the temporal discretization of the equation using C-N Scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical result...

This paper presents a discussion on the properties of collocation meshfree method, Updated Lagrangian Taylor-SPH (UL-TSPH), for dynamic problems in solid mechanics. The PDEs are written mixed form terms stress and velocity elastodynamics problems. Two sets particles used to discretize partial differential equations, resulting avoiding tensile instability inherent classical SPH formulations. Num...

The paper provides a computational technique that allows to compare all linear methods for PDE solving that use the same input data. This is done by writing them as linear recovery formulas for solution values as linear combinations of the input data, and these formulas are continuous linear functionals on Sobolev spaces. Calculating the norm of these functionals on a fixed Sobolev space will t...