[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 …

A novel RBF-based meshless method for solving time-fractional transport equations in 2D and 3D arbitrary domains

J Lin, J Bai, S Reutskiy, J Lu - Engineering with Computers, 2023 - Springer
In this paper, we develop a new meshless method for solving a wide class of time-fractional
partial differential equations with general space operators in 2D and 3D regular and …

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 …

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 …

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 …

A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation

S Abbasbandy, HR Ghehsareh, I Hashim - Engineering Analysis with …, 2013 - Elsevier
In this paper, an efficient numerical technique is developed to approximate the solution of
two-dimensional cubic nonlinear Schrödinger equations. The method is based on the …

Meshless simulations of the two-dimensional fractional-time convection–diffusion–reaction equations

A Shirzadi, L Ling, S Abbasbandy - Engineering analysis with boundary …, 2012 - Elsevier
The aim of this work is to propose a numerical approach based on the local weak
formulations and finite difference scheme to solve the two-dimensional fractional-time …

Analysis of meshless local and spectral meshless radial point interpolation (MLRPI and SMRPI) on 3-D nonlinear wave equations

E Shivanian - Ocean Engineering, 2014 - Elsevier
In this paper, the meshless local radial point interpolation (MLRPI) method is applied to
simulate three space dimensional nonlinear wave equation of the form u tt+ α u t+ β u= u xx+ …