In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...

This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for functions from their data. Well-posedness of the problem means that this recovery is continuous. Discretization recovers restricted trial functions from restricted test data, and it is well-posed or stable, ...

We study transient thermoelastic deformations of a thick functionally graded plate with edges held at a uniform temperature and either simply supported or clamped. Either the temperature or the heat flux is prescribed on the top surface of the plate with the bottom surface of the plate kept at either a uniform temperature or thermally insulated. Stresses and deformations induced due to the simu...

A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral repr...

The Meshless Local Petrov Galerkin (MLPG) method is used to solve the non-steady two dimensional Navier-Stokes equations. Transient laminar flow field calculations have been carried out in domains wherein certain surfaces have: (i) a sliding motion, (ii) a harmonic motion, (iii) an undulatory movement, and (iv) a contraction-expansion movement. The weak form of the governing equations has been ...

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...

The meshless local radial point interpolation (MLRPI) method is applied to examine the magnetohydrodynamic (MHD) ow of third grade uid in a porous medium. The uid saturates the porous space between the two boundaries. Several limiting cases of fundamental ows can be obtained as the special cases of present analysis. The variations of pertinent parameters are addressed.

In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshl...