hossein pourbashash - Academia.edu (original) (raw)

Papers by hossein pourbashash

analysis of within host virus models with cell-to-cell

Scientific Reports, 2022

The multidisciplinary nature of piezoelectric (PZ) structures necessitates precise and efficient ... more The multidisciplinary nature of piezoelectric (PZ) structures necessitates precise and efficient methods to express their behavior under different conditions. This article extends the general usage of PZ materials by introducing acoustic and fluid loading effects in a way that an unfilled multilayer cylindrical nanoshell with a functionally graded (FG) material core and PZ layers is subjected to preliminary external electric load, acoustic waves and external flow motion. As the properties of a functionally graded material changes along the shell thickness, a power law model is assumed to be governing such variations of desired characteristics. Evidently, this system includes different types of couplings and a comprehensive approach is required to describe the structural response. To this aim, the first-order shear deformation theory (FSDT) is used to define different displacement components. Next, the coupled size-dependent vibroacoustic equations are derived based on in conjunction...

$Research paper thumbnail of Computational Methods for Differential Equations Application of high-order spectral method for the time fractional mobile/immobile equation$

In this paper, a numerical efficient method is proposed for the solution of time fractional mobil... more In this paper, a numerical efficient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a finite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ 2−γ) for 0 < γ < 1. Also, we introduce the Legendre and shifted Legendre polynomials for full discretization. The aim of this paper is to show that the spectral method based on the Legendre polynomial is also suitable for the treatment of the fractional partial differential equations. Numerical examples confirm the high accuracy of proposed scheme.

$Research paper thumbnail of Application of high-order spectral method for the time fractional mobile/immobile equation$

Computational Methods for Differential Equations, 2016

In this paper, a numerical eﬃcient method is proposed for the solution of time fractional mobile/... more In this paper, a numerical eﬃcient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a ﬁnite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ2−γ) for 0 < γ < 1. Also, we introduce the Legendre and shifted Legendre polynomials for full discretization. The aim of this paper is to show that the spectral method based on the egendre polynomial is also suitable for the treatment of the fractional partial differential equations. Numerical examples conﬁrm the high accuracy of proposed scheme.

Tick-borne diseases (TBDs) a ect 80 of the world's cattle population, hampering livestockprod... more Tick-borne diseases (TBDs) a ect 80 of the world's cattle population, hampering livestockproduction throughout the world. In this article we will consider the Babesiosis disease inbovine and tick populations model. We conduct the local and global stability analysis of themodel. We present a dynamic behavior of this model using an ecient computational algo-rithm, namely the multistage modi ed sinc method(MMSM). The MMSM is used here as analgorithm for approximating the solutions of proposed system in a sequence of time intervals.In order to show the eciency of the method, the obtained numerical results are comparedwith the fourth-order Runge-Kutta method (RKM). It is shown that the MMSM has the ad-vantage of giving an analytical form of the solution within each time interval which is notpossible in purely numerical techniques like RKM.

In this paper we consider boundary value problems with singularity in equation or solution. To so... more In this paper we consider boundary value problems with singularity in equation or solution. To solve these problems, we apply single exponential and double exponential transformations of sinc-Galerkin and Chebyshev cardinal functions. Numerical examples highlight efficiency of Chebyshev cardinal functions and sinc-Galerkin method in problems with singularity in equations. It is illustrated that in problems with singular solutions, Chebyshev cardinal functions is not applicable. However, sinc-Galerkin method overcomes to this difficultly.

Tick-borne diseases (TBDs) aect 80 of the world's cattle population,hampering livestock produ... more Tick-borne diseases (TBDs) aect 80 of the world's cattle population,hampering livestock production throughout the world. In this article wewill consider the Babesiosis disease in bovine and tick populations model . We conduct the local and global stability analysis of the model .We present a dynamic behavior of this model using an ecient compu-tational algorithm, namely the multistage modied sinc method(MMSM).The MMSM is used here as an algorithm for approximating the solutions ofproposed system in a sequence of time intervals. In order to show the e-ciency of the method, the obtained numerical results are compared with thefourth-order Runge-Kutta method (RKM). It is shown that the MMSM hasthe advantage of giving an analytical form of the solution within each timeinterval which is not possible in purely numerical techniques like RKM.

International Journal of Numerical Methods for Heat & Fluid Flow, 2021

Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerica... more Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

Applied Mathematics and Computation, 2018

The main aim of this paper is to propose an efficient and suitable numerical procedure based on t... more The main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the two-dimensional modified anomalous sub-diffusion equation. The fractional derivative is based on the Riemann–Liouville fractional integral. Firstly, a finite difference scheme with O(τ) has been employed to discrete the time variable and also the local radial basis-finite difference (LRBF-FD) method is used to discrete the spatial direction. For the presented numerical technique, we prove the unconditional stability and also obtain an error bound. We employ a test problem to show the accuracy of the proposed technique. Also, we solve the mentioned model on irregular domain to show the efficincy of the developed technique.

Iranian Journal of Science and Technology, Transactions A: Science, 2018

Tick-borne diseases affect 80 of the world’s cattle population, hampering livestock production th... more Tick-borne diseases affect 80 of the world’s cattle population, hampering livestock production throughout the world. In this article, we will consider the Babesiosis disease in bovine and tick populations model. We conduct the local and global stability analysis of the model. We present a dynamic behavior of this model using an efficient computational algorithm, namely the multistage modified sinc method (MMSM). The MMSM is used here as an algorithm for approximating the solutions of proposed system in a sequence of time intervals. To show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge–Kutta method (RKM). It is shown that the MMSM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RKM.

$Research paper thumbnail of On solving fractional mobile/immobile equation$

Advances in Mechanical Engineering, 2017

In this article, a numerical efficient method for fractional mobile/immobile equation is develope... more In this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders [Formula: see text] and [Formula: see text], respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.

Applied Mathematics, 2016

In this paper, we apply the new algorithm of reproducing kernel method to give the approximate so... more In this paper, we apply the new algorithm of reproducing kernel method to give the approximate solution to some functional-differential equations. The numerical results demonstrate the accuracy of the proposed algorithm.

Discrete and Continuous Dynamical Systems - Series B, 2014

Computational Methods for Differential Equations, 2018

A mathematical model of a within-host viral infection is presented. A local stability analysis of... more A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there exists a unique infectious equilibrium which may or may not be stable. In the case of instability, there exists an asymptotically stable periodic solution. Secondly, an analysis of local center manifold shows that when R0 = 1, a transcritical bifurcation occurs where upon increasing R0 greater than one the DFE loses stability and a locally asymptotically positive infection equilibrium appears.

International Journal of Mathematical Modelling & Computations, 2017

The sinc method is known as an ecient numerical method for solving ordinary or par-tial di erent... more The sinc method is known as an ecient numerical method for solving ordinary or par-tial di erential equations but the system of di erential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical models in disease, the detailed stability analyses and numerical experiments are given on the standard within-host virus infections model.

International Journal of Mathematical Modelling & Computations, 2014

Spectral approximations for ODEs in unbounded domains have only received limited attention. In ma... more Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability of the sinc-collocation method in overcoming the singular points difficulties makes it an efficient method in dealing with these equations. We use numerical examples to highlight efficiency of sinc-collocation method in problems with singularity in equations.

World Academy of Science, Engineering and Technology, International Journal of Bioengineering and Life Sciences, 2015

$Research paper thumbnail of The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains$

International Journal of Numerical Methods for Heat & Fluid Flow

Purpose This study aims to propose a new numerical method for solving non-linear partial differen... more Purpose This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains. Design/methodology/approach The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space. Findings First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders O(τ1+γ) and O(τ2−γ) for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique. Originality/value The proposed numerical tech...