Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Approximation algorithm for maximum flow network interdiction problemالگوریتم تقریبی برای مساله ممانعت از بیشترین جریان شبکه1182505710.22067/ijnao.v10i1.75392ENM. AfshariradDepartment of Mathematics, University of Science and Technology of Mazandaran, P.O.Box: 48518-78195, Behshahr, Iran.Journal Article20180915We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Axial preferred solutions for multiobjective optimal control problems: An application to chemical processes19322507510.22067/ijnao.v10i1.75932ENG.H. AskarirobatiDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.A.H. BorzabadiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran.A. HeydariDepartment of Mathematics, Payame Noor University, Mashhad, Iran.0000-0002-8740-2621Journal Article20181012Detecting 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401An efficient algorithm to improve the accuracy and reduce the computations of LS-SVM33472509210.22067/ijnao.v10i1.75061ENM. BaymaniDepartment of Computer and Mathematics, Quchan University of Advanced Technology, Quchan, Iran.0000-0002-7066-0333A. MansooriDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20180831We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Using 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 بالا49622511410.22067/ijnao.v10i1.80682ENJ. BiazarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.M. DehghanDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.T. HoulariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.Journal Article20190514We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401The Fibonacci polynomials solution for Abel’s integral equation of second kind63792513810.22067/ijnao.v10i1.81828ENH. Deilami AzodiFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.0000-0002-6314-025XJournal Article20190709We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Quasi Interpolation of radial basis functions-pseudospectral method for solving nonlinear Klein–Gordon and sine-Gordon equations811062516510.22067/ijnao.v10i1.75129ENM. EmamjomehDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.S. AbbasbandyDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.0000-0003-3385-4152D. RostamyDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.Journal Article20180906We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401A 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 ای1071202518410.22067/ijnao.v10i1.79654ENH.S. AmiriDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.A.H. BorzabadiDepartment of Applied Mathematics, University of Science and Technology of Mazandaran, P.O. Box 48518-78195, Behshahr, Iran.A. HeydariDepartment of Mathematics, Payame Noor University, Mashhad, Iran.0000-0002-8740-2621Journal Article20190311We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401A new method for exact product form and approximation solutions of a parabolic equation with nonlocal initial condition using Ritz method1211382520810.22067/ijnao.v10i1.83685ENZ. BarikbinDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran,Journal Article20191009Many 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Moving to higher directional scheduling schemes1391552522310.22067/ijnao.v10i1.73001ENH.R. YousefzadehDepartment of Mathematics, Payame Noor University (PNU), Iran.0000-0002-9850-2900M. NasehiDepartment of Mathematics, Payame Noor University (PNU), Iran.Journal Article20191001A 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Application of control and optimal treatment for predator-prey model†1571762524610.22067/ijnao.v10i1.84901ENM.H. Rahmani DoustDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran.0000-0001-6603-5503M. ShirazianDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran.0000-0003-3121-3722M. ShamsabadiDepartment of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran.Journal Article20200101Mathematical 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401On the stabilization of a coupled fractional ordinary and partial differential equations†1771932526610.22067/ijnao.v10i1.84902ENS. AmiriDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.M. KeyanpourFaculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.0000-0002-6499-2489Journal Article20200101We 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697710120200401Shifted Jacobi collocation scheme for multidimensional time-fractional order telegraph equation1952232527810.22067/ijnao.v10i1.82774ENR.M. HafezDepartment of Mathematics, Faculty of Education, Matrouh University, Matrouh, Egypt.Y.H. YoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.0000-0003-0403-8797Journal Article20190901We 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.