[PDF][PDF] Applications of the MLPG method in engineering & sciences: a review

J Sladek, P Stanak, ZD Han, V Sladek… - … : Computer Modeling in …, 2013 - Citeseer
A review is presented for analysis of problems in engineering & the sciences, with the use of
the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods …

On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three‐dimensional wave equations

E Shivanian - International Journal for Numerical Methods in …, 2016 - Wiley Online Library
In this article, the meshless local radial point interpolation method is applied to analyze three
space dimensional wave equations of the form subject to given initial and Dirichlet boundary …

Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection–diffusion equations

F Mirzaee, N Samadyar - Engineering with computers, 2020 - Springer
The present article develops a semi-discrete numerical scheme to solve the time-fractional
stochastic advection–diffusion equations. This method, which is based on finite difference …

Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with dam**

VR Hosseini, E Shivanian, W Chen - Journal of Computational Physics, 2016 - Elsevier
The purpose of the current investigation is to determine numerical solution of time-fractional
diffusion-wave equation with dam** for Caputo's fractional derivative of order α (1< α≤ 2) …

Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation

VR Hosseini, E Shivanian, W Chen - The European Physical Journal Plus, 2015 - Springer
In this article, a general type of two-dimensional time-fractional telegraph equation
explained by the Caputo derivative sense for (1< α≤ 2) is considered and analyzed by a …

Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation

E Shivanian - Engineering Analysis with Boundary Elements, 2015 - Elsevier
This paper proposes an approach based on the Galerkin weak form and moving least
squares (MLS) approximation to simulate three space dimensional nonlinear wave equation …

A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms

E Shivanian - Engineering Analysis with Boundary Elements, 2015 - Elsevier
In this article, a new spectral meshless radial point interpolation (SMRPI) technique is
proposed and, as a test problem, applied to the two-dimensional diffusion equation with an …

Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics

E Shivanian - Engineering Analysis with Boundary Elements, 2013 - Elsevier
In this paper the meshless local radial point interpolation (MLRPI) method is applied to
simulate a nonlinear partial integro-differential equation arising in population dynamics. This …

Numerical solution of time fractional stochastic Korteweg–de Vries equation via implicit meshless approach

F Mirzaee, N Samadyar - Iranian Journal of Science and Technology …, 2019 - Springer
In this article, a numerical scheme is implemented to approximate the solution of time
fractional stochastic Korteweg–de Vries (KdV) equation. The structure of the proposed …

A computational meshfree RPIM approach for phase-field modeling of brittle fracture

H Saberi, CT Nguyen, H Saberi, M Sabagh… - Acta Mechanica, 2024 - Springer
Modeling failure mechanisms in solids by using sharp crack discontinuities suffers various
shortcomings that can be diminished by diffusive crack conception or phase-field method …