A review of operational matrices and spectral techniques for fractional calculus

AH Bhrawy, TM Taha, JAT Machado - Nonlinear Dynamics, 2015 - Springer
Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …

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 …

An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein–Gordon equations

M Dehghan, M Abbaszadeh, A Mohebbi - Engineering Analysis with …, 2015 - Elsevier
In this paper, we propose a numerical method for the solution of time fractional nonlinear
sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum …

Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier–Stokes equation

M Dehghan, M Abbaszadeh - Computer Methods in Applied Mechanics …, 2016 - Elsevier
Recently, because of simplicity of meshless methods, they have been employed for solving
many partial differential equations. One of the meshless methods is element free Galerkin …

An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate

M Abbaszadeh, M Dehghan - Numerical Algorithms, 2017 - Springer
In the current decade, the meshless methods have been developed for solving partial
differential equations. The meshless methods may be classified in two basic parts: 1. The …

[HTML][HTML] RBF-based local meshless method for fractional diffusion equations

M Irfan, FM Alotaibi, S Haque, N Mlaiki, K Shah - Fractal and Fractional, 2023 - mdpi.com
The fractional diffusion equation is one of the important recent models that can efficiently
characterize various complex diffusion processes, such as in inhomogeneous or …

The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations

M Dehghan, M Abbaszadeh - Journal of Computational Physics, 2017 - Elsevier
The main aim of this paper is to develop a fast and efficient local meshless method for
solving shallow water equations in one-and two-dimensional cases. The mentioned …

Numerical study of nanofluid flow and heat transfer over a rotating disk using Buongiorno's model

JA Khan, M Mustafa, T Hayat… - International Journal of …, 2017 - emerald.com
Purpose The purpose of the present study is to explore a three-dimensional rotating flow of
water-based nanofluids caused by an infinite rotating disk. Design/methodology/approach …

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 …

[HTML][HTML] Error estimate for the numerical solution of fractional reaction–subdiffusion process based on a meshless method

M Dehghan, M Abbaszadeh, A Mohebbi - Journal of Computational and …, 2015 - Elsevier
In this paper a numerical technique based on a meshless method is proposed for solving the
time fractional reaction–subdiffusion equation. Firstly, we obtain a time discrete scheme …