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...

A localized virtual boundary element–meshless collocation method (LVBE-MCM) is proposed to solve Laplace and Helmholtz equations in complex two-dimensional (2D) geometries. “Localized” refers employing the moving least square locally approximate physical quantities of computational domain after introducing traditional element method. The LVBE-MCM a semi-analytical domain-type meshless that base...

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...

Abstract In this paper, we propose the meshless finite point method for solving a type of fluid flow problem. The moving least square function is combined with collocation to treat nonlinear one- and two-dimensional soil water-salt movement equations. An adaptive windward scheme used stabilize numerical solution in regions large gradient change. Numerical examples comparison among proposed meth...

In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM meshless and easy-to-implement in complex geometries higher dimensions, therefore, it highly demanding. the Caputo derivative of order ? (0, 1] used to approximate first whereas, Crank-Nicolson scheme hired space derivatives. numerical solutions are p...

We propose a new and simple technique called the Symmetric Smoothed Particle Hydrodynamics (SSPH) method to construct basis functions for meshless methods that use only locations of particles. These basis functions are found to be similar to those in the Finite Element Method (FEM) except that the basis for the derivatives of a function need not be obtained by differentiating those for the func...