2225Vol 10, No 1, (2020), Serial Number: 1710120202020-04-05
Research ArticlearticlesartART
10.22067/ijnao.v10i1.75392Approximation algorithm for maximum flow network interdiction problemالگوریتم تقریبی برای مساله ممانعت از بیشترین جریان شبکهWe consider the maximum flow network interdiction problem. We provide a new interpretation of the problem and define a concept called ”optimalcut”. We propose a heuristic algorithm to obtain an approximated cut, and we also obtain its error bound. Finally, we show that our heuristic is an α-approximation algorithm for a class of networks. By implementing it on three network types, we show the advantage of it over solving the model by CPLEX.در این مقاله به بررسی مساله ممانعت از بیشترین جریان شبکه می‌پردازیم. نخست تعبیر جدیدی از مساله را ارائه داده و سپس مفهوم "برش بهینه" را تعریف می‌کنیم. یک الگوریتم ابتکاری برای یافتن تقریبی از برش بهینه پیشنهاد می‌کنیم. در نهایت نشان خواهیم داد که روش ابتکاری پیشنهادی برای نوع خاصی از شبکه‌ها، تبدیل به یک الگوریتم آلفا-تقریب خواهد شد. با اجرای الگوریتم بر روی سه نوع شبکه مختلف، برتری این روش را نسبت به حل مستقیم مدل بااستفاده از CPLEX نشان خواهیم داد.MariaAfshariradDepartment of Mathematics, University of Science and Technology of Mazandaran, P.O.Box: 48518-78195, Behshahr, Iran.دانشگاه علم و فناوری مازندرانIRm.afsharirad@mazust.ac.ir1-182020-03-18360703
10.22067/ijnao.v10i1.75932Axial preferred solutions for multiobjective optimal control problems: An application to chemical processesDetecting the Pareto optimal solutions on the Pareto frontier is one of the most important topics in multiobjective optimal control problems. In real-world control systems, there is needed for the decision-maker to apply their own opinion to find the preferred solution from a large list of Pareto optimal solutions. This paper presents a class of axial preferred solutions for multiobjective optimal control problems in contexts in which partial information on preference weights of objectives is available. These solutions combine both the idea of improvement axis and Pareto optimality with respect to preference information. The axial preferred solution, in addition to taking considerations of decision-makers, provides continuous functions for control ling chemical processes. Numerical results are presented for two problems of chemical processes with two different preferential situations.Gholam H.AskarirobatiDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.دانشگاه پیام نور تهران‎ P.O.Box 19395-3697IRaskari@phd.pnu.ac.irAkbarHashemi BorzabadiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran.IRborzabadi@du.ac.irAghilehHeydari‎‎‎Department of Mathematics, Payame Noor University, Mashhad, Iran.دانشگاه پیام نورIRa_heidari@pnu.ac.ir19-322020-03-18360702
10.22067/ijnao.v10i1.75061An efficient algorithm to improve the accuracy and reduce the computations of LS-SVMیک الگوریتم کارآمد برای بهبود دقت و کاهش محاسبات کمترین مربعات بردار پشتیبانWe present a novel algorithm, which is called Cutting Algorithm (CA), for improving the accuracy and reducing the computations of the Least Squares Support Vector Machines (LS-SVMs). The method is based on dividing the original problem to some subproblems. Since a master problem is converted to some small problems, so this algorithm has fewer computations. Although, in some cases that the typical LS-SVM cannot classify the dataset linearly, applying the CA the datasets can be classified. In fact, the CA improves the accuracy and reduces the computations. The reported and comparative results on some known datasets and synthetics data demonstrate the efficiency and the performance of CA.MojtabaBaymaniDepartment of Computer and Mathematics, Quchan University of Advanced Technology, Quchan, Iran. IRm_baymani@qiet.ac.irAminMansooriDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.IRa-mansoori@um.ac.ir33-472020-03-18360701
10.22067/ijnao.v10i1.80682Using homotopy analysis method to find the eigenvalues of higher order fractional Sturm–Liouville problemsبه کارگیری روش آنالیز هموتوپی برای یافتن مقادیر ویژه مسأله اشتورم-لیوویل کسری از مرتبه بالا We utilize the homotopy analysis method to find eigenvalues of fractional Sturm–Liouville problems. Inasmuch as very few papers have been devoted to estimating eigenvalues of these kind of problems, this work enjoys a particular significance in many different branches of science. The convergence of the homotopy analysis method is also considered on the high order fractional Sturm–Liouville problem. The numerical results acknowledge the ability of the proposed method. Eigenvalues are computed within a couple of minutesCPU time at core i3, 2.7 GHz PC.JafarBiazarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran. IRjafar.biazar@gmail.comMohammadDehghanDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.IRdehghan@iausari.ac.irTaherehHoulariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.IRtahereh.houlari@gmail.com49-622020-03-18360699
10.22067/ijnao.v10i1.81828The Fibonacci polynomials solution for Abel’s integral equation of second kindجواب چندجمله‌ای‌های فیبوناچی برای معادله‌ی انتگرالی آبل نوع دومWe suggest a convenient method based on the Fibonacci polynomials and the collocation points for solving approximately the Abel’s integral equation of second kind. Initially, the solution is supposed in the form of the Fibonacci polynomials truncated series with the unknown coefficients. Then, by placing this series into the main problem and collocating the resulting equation at some points, a system of algebraic equations is obtained. After solving it, the unknown coefficients and so the solution of main problem are determined. The error analysis is discussed elaborately. Also, the reliability of the method is quantified through numerical examples.در این مقاله، روشی آسان بر اساس چندجمله‌ای‌های فیبوناچی و نقاط هم‌مکانی برای حل معادله‌ی انتگرالی آبل نوع دوم پیشنهاد می‌گردد. ابتدا جواب به شکل سری بریده شده‌ی چندجمله‌ای‌های فیبوناچی با ضرایب نامعلوم فرض می‌شود. سپس با جای‌گذاری این سری در مسأله‌ی اصلی و هم‌مکانی نمودن معادله‌ی حاصل در چندین نقطه، دستگاهی از معادلات جبری به دست می‌آید. پس از حل آن، ضرایب نامعلوم و همین‌طور جواب مسأله‌ی اصلی تعیین می‌شوند. آنالیز خطا به صورت دقیق مورد بحث قرار می‌گیرد. همچنین، اعتبار روش&nbsp; از طریق مثال‌هایی عددی سنجیده می‌شود&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;HamanDeilami AzodiFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.IRhaman.d.azodi@gmail.com63-792020-03-18360698
10.22067/ijnao.v10i1.75129Quasi Interpolation of radial basis functions-pseudospectral method for solving nonlinear Klein–Gordon and sine-Gordon equationsWe propose a new approach for solving nonlinear Klein–Gordon and sine-Gordon equations based on radial basis function-pseudospectralmethod (RBF-PS). The proposed numerical method is based on quasiinterpolation of radial basis function differentiation matrices for thediscretization of spatial derivatives combined with Runge–Kutta time stepping method in order to deal with the temporal part of the problem.The method does not require any linearization technique; in addition, a new technique is introduced to force approximations to satisfy exactlythe boundary conditions. The introduced scheme is tested for a number of one- and two-dimensional nonlinear problems. Numerical results andcomparisons with reported results in the literature are given to validate the presented method, and the reported results show the applicabilityand versatility of the proposed method.M. EmamjomehDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.IRemam_me@yahoo.comS.AbbasbandyDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. IRabbasbandy@yahoo.comD. RostamyDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. IRrostamy@khayam.ut.ac.ir81-1062020-03-18360697
10.22067/ijnao.v10i1.79654A different view on controllability and observability of continuous time linear systems with interval coefficientsنگاهی متفاوت به کنترل پذیری و مشاهده پذیری سیستمهای با تغییر زمان خطی همراه با ضرایب بازه ایWe discuss the controllability and observability of time-invariant (continuous time) linear systems with interval coefficients using the notion of being full rank of interval matrices. The most important advantage of the proposed attitude is to consider these two essential concepts, that is, control lability and observability, in interval time-invariant linear systems, which, in turn, may play important roles in the analysis of uncertain systems. Some different definitions on to be full rank of matrices have been utilized to propose different views on the controllability and observability of interval linear systems according to different criteria. Finally, in several control-observation processes, the controllability and observability are evaluated based on the given achievements.Hadi S.AmiriDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.IRh.shokoohi53@gmail.comAkbarH. BorzabadiDepartment of Applied Mathematics, University of Science and Technology of Mazandaran, P.O. Box 48518-78195, Behshahr, Iran.IRborzabadi@mazust.ac.irAghileh HeydariDepartment of Mathematics, Payame Noor University, Mashhad, Iran. IRa_heidari@pnu.ac.ir107-1202020-03-18360696
10.22067/ijnao.v10i1.83685A new method for exact product form and approximation solutions of a parabolic equation with nonlocal initial condition using Ritz method Many phenomena in various fields of physics are simulated by parabolic partial differential equations with the nonlocal initial conditions, while there are few numerical methods for solving these problems. In this paper, the Ritz–Galerkin method with a new approach is proposed to give the exact and approximate product solution of a parabolic equation with the nonstandard initial conditions. For this purpose, at first, we introduce a function called satisfier function, which satisfies all the initial and boundary conditions. The uniqueness of the satisfier function and its relation to the exact solution are discussed. Then the Ritz–Galerkin method with satisfier function is used to simplify the parabolic partial differential equations to the solution of algebraic equations. Error analysis is worked by using the property of interpolation. The comparisons of the obtained results with the results of other methods show more accuracy in the presented technique. ZahraBarikbinDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran,IRbarikbin@sci.ikiu.ac.ir121-1382020-03-18360695
10.22067/ijnao.v10i1.73001Moving to higher directional scheduling schemes A general overview of the scheduling’s literature of some researches shows that among various factors, the priority rules and also the structure of projects are two main factors that can be affected on the performance of multidirectional scheduling schemes. In addition, a variation on the number of directors in scheduling schemes (e.g., single directional, bi-directional, and tri-directional scheduling scheme) produces different makespans. However, the question of when to move from the single direction to the multidirectional scheduling schemes remained open. In this paper, based on analytical and also empirical results, we show that when availability and distributions of resource measures such as the number of peaks and number of overflows or the average amount of overflows are increased, higher directional scheduling schemes can be produced smaller makespans. Hence, in the light of these resource measures, the multidirectional scheduling schemes can be reduced the dependency of the solution’s quality on the priority rules used.Hamid RezaYousefzadeDepartment of Mathematics, Payame Noor University (PNU), Iran. IRusefzadeh.math@pnu.ac.irMaryamNasehiDepartment of Mathematics, Payame Noor University (PNU), Iran.IRmaryam5787@gmail.com139-1552020-03-18360694
10.22067/ijnao.v10i1.84901Application of control and optimal treatment for predator-prey model†Mathematical ecology and mathematical epidemiology are major fields in both biology and applied mathematics. In the present paper, a fourdimensional eco-epidemiological model with infection in both prey and preda tor populations is studied. It consists of susceptible prey, infected prey, susceptible predator, and infected predator. The functional response is assumed to be of Lotka–Volterra type. The behavior of the system such as the existence, boundedness, and stability for solutions and equilibria are studied and also the basic reproduction number for the proposed model is computed. Moreover, a related control model and optimal treatment for the control model are presented. Finally, to verify the analytical discussion, a numerical simulation is carried out.M.H. Rahmani DoustDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran.IRmh.rahmanidoust@neyshabur.ac.ir M.ShirazianDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran. IRshirazian@neyshabur.ac.irM. ShamsabadiDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran. IRshamsabadi@neyshabur.ac.ir157-1762020-03-18360693
10.22067/ijnao.v10i1.84902On the stabilization of a coupled fractional ordinary and partial differential equations†We investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional diffusion (FD) equation, where the interconnections are of Neumann type. We exploit the PDE back stepping method as a powerful tool for designing a controller to show the Mittag–Leffler stability of the FD-FODE cascade. Finally, numerical simulations are presented to verify the results.Shadi AmiriDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. IRamiri_shadi@phd.guilan.ac.irMohammadKeyanpourFaculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.IRkianpour@guilan.ac.ir177-1932020-03-18360691
10.22067/ijnao.v10i1.82774Shifted Jacobi collocation scheme for multidimensional time-fractional order telegraph equationWe propose a numerical scheme to solve a general class of time-fractional order telegraph equation in multidimensions using collocation points nodes and approximating the solution using double shifted Jacobi polynomials. The main characteristic behind this approach is to investigate a time-space collocation approximation for temporal and spatial discretizations. The applica bility and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple, applicable, and accurate.R.M.HafezDepartment of Mathematics, Faculty of Education, Matrouh University, Matrouh, Egypt.EGr_mhafez@yahoo.comY.H.YoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.EGyoussri@sci.cu.edu.eg195-2232020-03-18360690