Papers by Mohammad Ali Fariborzi Araghi
Journal of Intelligent & Fuzzy Systems
Mathematical modeling of many natural and physical phenomena in industry, engineering sciences an... more Mathematical modeling of many natural and physical phenomena in industry, engineering sciences and basic sciences lead to linear and non-linear devices. In many cases, the coefficients of these devices, taking into account qualitative or linguistic concepts, show their complexity in the form of Z-numbers. Since Z-number involves both fuzziness and reliability or probabilistic uncertainty, it is difficult to obtain the exact solution to the problems with Z-number. In this work, a method and an algorithm are proposed for the approximate solution of a Z-number linear system of equations as an important case of such problems. The paper is devoted to solving linear systems where the coefficients of the variables and right hand side values are Z-numbers. An algorithm is presented based on a ranking scheme and the neural network technique to solve the obtained system. Moreover, two examples are included to describe the procedure of the method and results.
Journal of Linear and Topological Algebra, May 1, 2015
One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy ana... more One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to find the approximate solution of some systems of PDEs. Also, we show the region of convergence by plotting the H-surface.
Journal of Mathematical Extension, 2021
Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and e... more Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.
International Journal of Mathematical Modelling & Computations, 2012
The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX ... more The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX + XB = C where A = (aij) 2 R n n , B = (bij) 2 R m m are crisp M- matrices, C = (cij) 2 R n m is fuzzy matrix and X 2 R n m is unknown,by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At rst, we transform this system to an (mn) � (mn) fuzzy system of linear equations. Then, we convert this system to three (mn) � (mn) crisp linear systems of equations, and we solve them simultaneously by ABS algorithm.
Cumhuriyet Science Journal, 2015
Abstract. In this work, the homotopy analysis method (HAM) is applied to solve the fuzzy Black-Sc... more Abstract. In this work, the homotopy analysis method (HAM) is applied to solve the fuzzy Black-Scholes equation. Also, a theorem is proved to illustrate the convergence of the proposed method and two sample examples are solved by this method to verify the efficiency and importance of the method.
Journal of Linear and Topological Algebra, 2014
In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homo- topy analysis method ... more In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homo- topy analysis method (HAM) is investigated. A theorem is proved to guarantee the conver- gence of HAM and to nd the series solution of this equation via a reliable algorithm.
Discrete Dynamics in Nature and Society, 2020
This work introduces a novel modification of classical perturbation method (PM), denominated Opti... more This work introduces a novel modification of classical perturbation method (PM), denominated Optimized Distribution of Boundary Conditions Perturbation Method (ODBCPM) with the purpose to improve the performance of PM in the solution of ordinary differential equations (ODES). We will see that the main proposal of ODBCPM rests above all in the redistribution and optimization of the boundary conditions of the problem to be solved among the iterations of the proposed method. The solution of a couple of heat relevant problems indicates the potentiality of ODBCPM even for the case of large values of the perturbative parameter.
Asian Journal of Mathematics and Computer Research, 2015
Journal of Mathematical Extension, 2020
An efficient family of the recursive methods of adaptive is proposed for solving nonlinear equati... more An efficient family of the recursive methods of adaptive is proposed for solving nonlinear equations, is developed such that all previous information are applied. These methods have reached the maximum degree of convergence improvement of 100%, and also have an efficiency index of 2. Three families have been examined from Steffensen-Like single, two, and three-step methods that have used 2, 3 and 4 parameters respectively. Numerical comparisons are made with other existing methods one-, two-, three-, and four-point to show the performance of the convergence speed of the proposed method and confirm theoretical results.
Inverse Problems in Science and Engineering, 2021
ABSTRACT Constructing a matrix by its spectral information including singular values is called in... more ABSTRACT Constructing a matrix by its spectral information including singular values is called inverse singular value problem (ISVP). In this paper, an ISVP for nonsymmetric ahead arrow matrix by two eigenpairs of the required matrix and one singular value of each leading principal submatrices is investigated. To solve the problem, the recurrence relation of characteristic polynomial of the block Jordan–Weilant matrix associated with the aim matrix is obtained. The conditions of solvability of the problem are derived. Finally a numerical algorithm and an example are given.
Advances in Intelligent Systems and Computing, 2021
International Journal of Industrial Mathematics, 2020
In this work, the absolute value equation (AVE) $ Ax-vert x vert= b$ is solved by the Gauss-Seide... more In this work, the absolute value equation (AVE) $ Ax-vert x vert= b$ is solved by the Gauss-Seidel and Jacobi iterative methods based on the stochastic arithmetic, where $A$ is an arbitrary square matrix whose singular values exceed one. An algorithm is proposed to find the optimal number of iterations in the given iterative scheme and obtain the optimal solution with its accuracy. To this aim, the CESTAC $^{1}$footnote{Controle et Estimation Stochastique des Arrondis de Calculs} method and the CADNA $^{2}$footnote{Control of Accuracy and Debugging for Numerical Application} library are applied which allows us to estimate the round-off error effect on any computed result. The classical criterion to terminate the iterative procedure is replaced by a criterion independent of the given accuracy $(epsilon)$ such that the best solution is evaluated numerically. Numerical examples are solved to validate the results and show the efficiency and importance of using the stochastic arithmetic ...
International Journal of Mathematical Modelling & Computations, 2013
In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm ty... more In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.
International Journal of Mathematical Modelling & Computations, 2013
Integrating various suppliers to satisfy market demand is of great importance for e ective supply... more Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the accuracy of the proposed method with different choices of time and space meshes.
IEEE Transactions on Fuzzy Systems, 2019
In the present study, a new iterative numerical method for solving bivariate nonlinear fuzzy Fred... more In the present study, a new iterative numerical method for solving bivariate nonlinear fuzzy Fredholm integral equations is proposed. The method combines two well proven approaches: successive approximations and mixed trapezoidal and midpoint rules for the numerical integration. Both approaches are elaborated for fuzzy-valued functions. The main advantage of the proposed approach is that being targeting the particular equation, another subordinate problem was solved under the common constraints. By this, we mean the development of a numerical method for fuzzy integrals. As a result, the proposed method is more accurate in comparison with any other mechanical combination of two separate and independent methods. We give conditions for the existence and uniqueness of a solution and estimate the error of the obtained approximation. We prove stability and method is performed on test problems due to verify our theoretical results, and numerical results are compared with those from existing methods in the literature to confirm the accuracy and efficiency of the proposed method. Index Terms-Nonlinear two-dimensional fuzzy Fredholm integral equations, Iterative numerical method, Trapezoidal and midpoint rules.
Fuzzy Information and Engineering, 2014
East Journal on Approximations, 2009
Mathematical Sciences, 2021
Operational risk is one of the common risks in organizations, especially in banks, which has a wi... more Operational risk is one of the common risks in organizations, especially in banks, which has a wide range of errors in individual performance or system failure with process problems. In this paper, the mathematical model of operational risk to calculate the probability of the organization being convinced is presented, which is in the form of a Volterra integro-differenial equations and is solved by the Adomian decomposition method (ADM). Also, the ADM is applied in one dimension as semi-Adomian decomposition method (s-ADM). Comparison of results demonstrates proficiency of the ADM and s-ADMin this model.
The problem of constructing a matrix by its spectral information is called inverse eigenvalue pro... more The problem of constructing a matrix by its spectral information is called inverse eigenvalue problem (IEP) which arises in a variety of applications. In this paper, we study an IEP for arrowhead matrices in different cases. The problem involves constructing of the matrix by some eigenvalues of each of the leading principal submatrices and one eigenpair. We will also investigate this problem and its variants in the cases of matrix entries being real, nonnegative, positive definite, complex and equal diagonal entries. To solve the problems, a new method to establish a relationship between the IEP and properties of symmetric and general form of matrices is developed. The necessary and sufficient conditions of the solvability of the problems are obtained. Finally, some numerical examples are presented.
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Papers by Mohammad Ali Fariborzi Araghi