Papers by Elham Hashemizadeh
Computers & Mathematics with Applications, 2010
A quadrature rule based on uniform Haar wavelets and hybrid functions is proposed to find approxi... more A quadrature rule based on uniform Haar wavelets and hybrid functions is proposed to find approximate values of definite integrals. The wavelet-based algorithm can be easily extended to find numerical approximations for double, triple and improper integrals. The main advantage of this method is its efficiency and simple applicability. Error estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method.
Mathematical Researches, 2020
ArXiv, 2021
The present study proposed a method for numerical solution of linear Volterra integral equations ... more The present study proposed a method for numerical solution of linear Volterra integral equations (VIEs) of the third kind, before only analytical solution methods had been discussed with reference to previous research and review of the related literature. Given that such analytical solutions are not almost always feasible, it is required to provide a numerical method for solving the mentioned equations. Accordingly, Krall-Laguerre polynomials were utilized for numerical solution of these equations. The main purpose of this method is to approximate the unknown functions through Krall-Laguerre polynomials. Moreover, an error analysis is performed on the proposed method.
International Journal of Industrial Mathematics, 2016
In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has be... more In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and Block-Pulse functions which are orthonormal and have compact support on $[0, 1]$. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and effi...
International Journal of Industrial Mathematics, 2018
In this study, a new numerical solution of singular nonlinear differential equations, stemming fr... more In this study, a new numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is primarily based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. Furthermore, the convergence analysis on the proposed method is carried out. To assess the accuracy and analysis of performance of the method, five numerical problems, based on the singular nonlinear differential equations, on different subjects, such as the human head, Oxygen diffusion in a spherical cell and Bessel differential equation, were solved. The numerical results were compared with other existed methods in tables for verification and further discussions.
IET Intelligent Transport Systems, 2019
This article proposes an integrated system for segmentation and classification of two moving obje... more This article proposes an integrated system for segmentation and classification of two moving objects, including car and pedestrian from their side-view in a video sequence. Based on the use of grey-level co-occurrence matrix (GLCM) in Haar wavelet transformed space, the authors calculated features of texture data from different sub-bands separately. Haar wavelet transform is chosen because the resulting wavelet sub-bands are strongly affecting on the orientation elements in the GLCM computation. To evaluate the proposed method, the results of different sub-bands are compared with each other. Extracted features of objects are classified by using a support vector machine (SVM). Finally, the experimental results showed that use of three sub-bands of wavelets instead of two sub-bands is more effective and has good precision.
Physica A: Statistical Mechanics and its Applications, 2018
The numerous applications of time fractional partial differential equations in different fields o... more The numerous applications of time fractional partial differential equations in different fields of science especially in fluid mechanics necessitate the presentation of an efficient numerical method to solve them. In this paper, Galerkin method and operational matrix of fractional Riemann-Liouville integration for shifted Legendre polynomials has been applied to solve these equations. Some definitions for fractional calculus along with some basic properties of shifted Legendre polynomials have also been put forth. When approximations are substituted into the fractional partial differential equations, a set of algebraic equations would be resulted. The convergence of the suggested method was also depicted. In the end, the linear time fractional Klein-Gordon equation, dissipative Klein-Gordon equations and diffusion-wave equations were utilized as three examples so as to study the performance of the numerical scheme.
Journal of Modern Applied Statistical Methods, 2016
Legendre multiwavelets are introduced. These functions can be designed in such a way that the pro... more Legendre multiwavelets are introduced. These functions can be designed in such a way that the properties of orthogonality, polynomial approximation, and symmetry hold at the same time. In this way, they can be effectively deployed in image compression.
American Journal of Computational and Applied Mathematics, 2012
This paper proposed a numerical method for nonlinear singular ordinary differential equations, th... more This paper proposed a numerical method for nonlinear singular ordinary differential equations, that arises in biology and some diseases. We solved these nonlinear problems by a new method based on shifted Legendre polynomials. Operational matrices of derivatives for this function are presented to reduce the nonlinear singular boundary value problems to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are demonstrated through illustrative examples. The results obtained are compared by the known results.
Applied Mathematics and Computation, 2015
In this study, wavelet Galerkin method has been developed for solving nonlinear singular boundary... more In this study, wavelet Galerkin method has been developed for solving nonlinear singular boundary value problems associated with physiology science. The quasilinearization technique is applied to reduce the given nonlinear problem to a sequence of linear problems. We modify the resulting set of differential equations at the singular point then treat this set of boundary value problems by using compactly supported cubic B-spline wavelets and Galerkin method. These wavelets are used as testing and weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.
Communications in Nonlinear Science and Numerical Simulation, 2012
In this paper, we present a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equa... more In this paper, we present a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equations in terms of Bernstein polynomials. Properties of these polynomials and operational matrix of integration together with the product operational matrix are first presented. These properties are then utilized to transform the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Bernstein coefficients. The method is computationally very simple and attractive and numerical examples illustrate the efficiency and accuracy of the method.
Abstract—An approximation method based on operational matrices of Bernstein polynomials used for ... more Abstract—An approximation method based on operational matrices of Bernstein polynomials used for the solution of Hammerstein integral equations. The operational matrices of these functions are utilized to reduce a nonlinear Hammerstein and Volterra Hammerstein integral equation to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are demonstrated through illustrative examples. The results obtained are compared by the known results. Keywords: ...
Abstract—A new approach implementing Bernstein operational matrix method for the numerical soluti... more Abstract—A new approach implementing Bernstein operational matrix method for the numerical solution of differential equations, that arises in various physiology problems like oxygen diffusion, distribution of heat source in human head, tumor growth and etc. Operational matrix of derivative for Bernstein's polynomials function are presented to reduce these nonlinear differential equations to a system of nonlinear algebraic equation. Computational results are provided to demonstrate the viability of the new method. ...
AWERProcedia Information Technology and Computer Science, Dec 24, 2012
In this paper we proposed a new method for numerical solution of Fredholm and Volterra integral e... more In this paper we proposed a new method for numerical solution of Fredholm and Volterra integral equations by operational matrices of Bernstein polynomials. This method is very simple, accurate and attractive. Also we compared the proposed method results by some known method results to show the convergence and advantages of the Bernstein operational matrices method.
International Journal of the Physical Sciences, 2012
An approximation method based on hybrid Legendre polynomials and Block-Pulse functions used for t... more An approximation method based on hybrid Legendre polynomials and Block-Pulse functions used for the solution of nonlinear Volterra-Fredholm integral equations (NV-FIEs). The operational matrices of these functions are utilized to reduce a nonlinear Volterra-Fredholm integral equation to a system of nonlinear algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.
In this paper we introduce a new matrix method based on shifted Jacobi operational matrix for sol... more In this paper we introduce a new matrix method based on shifted Jacobi operational matrix for solving Lane – Emden type equations.TheLane – Emden type equationsarising in astrophysics. First we introduce the shifted Jocobi operational matrix of derivative and then by use of this operational matrix we numerically solved Lane – Emden type equations.Some illustrative examples are given to demonstrate the efficiency and validity of the proposed method.
Advances in Difference Equations, 2020
Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus.... more Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.
Symmetry, 2020
In this study, we present a spectral method for solving nonlinear Volterra integral equations wit... more In this study, we present a spectral method for solving nonlinear Volterra integral equations with weakly singular kernels based on the Genocchi polynomials. Many other interesting results concerning nonlinear equations with discontinuous symmetric kernels with application of group symmetry have remained beyond this paper. In the proposed approach, relying on the useful properties of Genocchi polynomials, we produce an operational matrix and a related coefficient matrix to convert nonlinear Volterra integral equations with weakly singular kernels into a system of algebraic equations. This method is very fast and gives high-precision answers with good accuracy in a low number of repetitions compared to other methods that are available. The error boundaries for this method are also presented. Some illustrative examples are provided to demonstrate the capability of the proposed method. Also, the results derived from the new method are compared to Euler’s method to show the superiority ...
In this paper, a practical and computational numerical method based on Bernstein polynomials for ... more In this paper, a practical and computational numerical method based on Bernstein polynomials for solving nonlinear stochastic integral equations is presented. Stochastic operational matrix of Bernstein polynomials is determined. The main idea is that it reduces the stochastic integral equation to a system of algebraic equations. Thus we can solve the problem by iteration methods. Numerical example illustrates the efficiency and accuracy of the method.
Uploads
Papers by Elham Hashemizadeh