Mohammad Ali Mehrpouya

Tafresh University · Department of Mathematics

Despite the significant advances in the numerical solution of nonlinear boundary value problems, most of the existing methods still encounter with a high sensitivity to the initial guess. The aim of this paper is to propose a less sensitive robust numerical scheme for accurate solution of sensitive boundary value problems. For this purpose, an orth...

It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton's method. Newton's method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. In this paper, a differential continuation method is presented for solving the nonlinear system o...

Despite the significant advances in the numerical solution of nonlinear boundary value problems, most of the existing methods still encounter with a high sensitivity to the initial guess. The aim of this paper is to propose a less sensitive robust numerical scheme for accurate solution of sensitive boundary value problems. For this purpose, an orth...

This paper addresses a magnetic yoke design to detect a notch on plate edges based on magnetic flux leakage. A design to detect a notch on plate edges is proposed in which magnetic flux leakage is used. To show the leaked magnetic field from the notch, a specimen with a high magnetic permeability is considered. Since in our setup the magnetic perme...

In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal control problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions...

In the present paper, a robust pseudospectral method for efficient numerical solution of nonlinear optimal control problems is presented. In the proposed method, at first, based on the Pontryagin's minimum principle, the first order necessary conditions of optimality which are led to the Hamiltonian boundary value problem are derived. Then, utilizi...

In the present paper, an efficient pseudospectral method for solving the Hamiltonian boundary value problems arising from a class of switching optimal control problems is presented. For this purpose, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality are derived. Then, by partitioning the time interval r...

Using backup plate is one of the most commonly used methods to decrease drilling-induced delamination of composite laminates. It has been shown that, the size of the delamination zone is related to the vertical element of cutting force named as thrust force. Also, direct control of thrust force is not a routine task, because, it depends on both dri...

In this paper, an efficient computational algorithm for the solution of Hamiltonian boundary value problems arising from bang-bang optimal control problems is presented. For this purpose, at first, based on the Pontryagin’s minimum principle, the first order necessary conditions of optimality are derived. Then, an indirect shooting method with cont...

In this paper, an efficient computational method for numerical solution of infinite horizon optimal control problems is presented. In the proposed method, transformed Legendre spectral scheme is utilized to transcribe the problem to a mathematical programming problem which can be solved by the well-developed optimization algorithms. The main advant...

In the present paper, an efficient pseudospectral method for the solution of two point boundary value problems arising in optimal control theory is presented. In the proposed method, the Gauss pseudospectral method is utilized to reduce a two point boundary value problem to the solution of a system of algebraic equations. However, convergence to th...

In the manuscript, a pseudospectral method is developed for approximate and efficient solution of nonlinear singular Lane-Emden-Fowler initial and boundary value problems arising in astrophysics. In the proposed method, the Gauss pseudospectral method is utilized to reduce the problem to the solution of a system of algebraic equations. Furthermore,...

We present an efficient computational procedure for the solution of bang–bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advant...

Our paper deals with an effective application of the pseudospectral method to solution of Hamiltonian boundary value problems in optimal control theory. The developed numerical methodology is based on the celebrated Gauss pseudospectral approach. The last one makes it possible to reduce the conventional Hamiltonian boundary value problem to an auxi...

We present an efficient computational procedure for the solution of bang–bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advant...

In the present paper, an efficient computational method for the solution of bang–bang optimal control problems is investigated. The method is based on control parametrization and belongs to the direct methods for numerical solution of optimal control problems. In this method, control functions are considered to be piecewise constant with values and...

In this work a numerical method for finding the optimal control of a time-delay system via a wavelets approach is discussed. We have chosen CAS wavelet functions as a family of orthogonal basis functions for our purpose. The properties of the CAS wavelets are presented. The operational matrices of integration, delay and product are given. These mat...

In this work a numerical method for finding the optimal control of a time-delay system via a wavelets approach is discussed. We have chosen CAS wavelet functions as a family of orthogonal basis functions for our purpose. The properties of the CAS wavelets are presented. The operational matrices of integration, delay and product are given. These mat...

In this work a numerical method for finding the optimal control of a time-delay system via a wavelets approach is discussed. We have chosen CAS wavelet functions as a family of orthogonal basis functions for our purpose. The properties of the CAS wavelets are presented. The operational matrices of integration, delay and product are given. These mat...

In this work a numerical method for finding the optimal control of a time-delay system via a wavelets approach is discussed. We have chosen CAS wavelet functions as a family of orthogonal basis functions for our purpose. The properties of the CAS wavelets are presented. The operational matrices of integration, delay and product are given. These mat...

In this paper, we present a computational method for solving Fredholm-Hammerstein integral equations of the second kind. The method utilizes CAS wavelets constructed on the unit interval as basis in the Galerkin method and reduces the solution of the Hammerstein integral equation to the solution of a nonlinear system of algebraic equations. Error a...

In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear sys...