University of GuilanJournal of Mathematical Modeling2345-394X10420221201Numerical methods based on spline quasi-interpolation operators for integro-differential equations387401557410.22124/jmm.2022.20181.1756ENChafikAllouchUniversity Mohammed I. FPN. MSC Team, LAMAO Laboratory, Nador, MoroccoDomingoBarreraDepartment of Applied Mathematics, University of Granada, Campus de Fuentenueva s/n, 18071 Granada, SpainMounaimSaouTeam ANAA, ANO Laboratory , Faculty of Sciences, University Mohammed First, Oujda, MoroccoDrissSbibihANO Laboratory , Faculty of Sciences, University Mohammed First, Oujda, MoroccoMohamedTahrichiTeam ANAA, ANO Laboratory , Faculty of Sciences, University Mohammed First, Oujda, Morocco0000-0001-7898-4503Journal Article20210717In this paper, we propose collocation and Kantorovich methods based on spline quasi-interpolants defined on a bounded interval to solve numerically a class of Fredholm integro-differential equations. We describe the computational aspects for calculating the approximate solutions and give theoretical results corresponding to the convergence order of each method in terms of the degree of the considered spline quasi-interpolant. Finally, we provide some numerical tests that confirm the theoretical results and prove the efficiency of the proposed methods.https://jmm.guilan.ac.ir/article_5574_92864f46bed933014de2c5a885b159c5.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Solvability of the fuzzy integral equations due to road traffic flow403415558010.22124/jmm.2022.21596.1895ENVahidSamadpour Khalifeh MahalehDepartment of Traffic Engineering, Amin Police University, Tehran, Iran0000-0002-9886-1030RezaEzatiDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20220125In this research, we investigate the fuzzy integral equations related to traffic flow. Using the Banach fixed point theorem, we prove the existence and uniqueness of the solution for such equations. Using the Picard iterative method, we obtain the upper bound for an accurate and approximate solution. Finally, we obtain an error estimation between the exact solution and the solution of the iterative method. Example shows the applicabilityof our results.https://jmm.guilan.ac.ir/article_5580_d10bafd21e0f0c583d6655d87e055282.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201A mathematical model to simulate the drug release pattern from drug-eluting stents with biostable polymeric bulk and hydrophobic incorporated drug417435559610.22124/jmm.2022.21157.1850ENHadisehKamalgharibiSchool of Mathematics and Computer Science, Damghan University, Damghan, IranAkbarHashemi BorzabadiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran & Department of Applied Mathematics, University of Science and Technology of Mazandaran, IranOmidSolaymani FardSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran & Faculty of Mathematical Science, Ferdowsi University, Mashhad, IranAtefehSolouk MofradDepartment of Biomedical Engineering, Amirkabir University of Technology, Tehran, IranMehdiShafieianDepartment of Biomedical Engineering, Amirkabir University of Technology, Tehran, IranJournal Article20211125DES, or drug-eluting stents, have the advantage of reducing restenosis rates relative to bare-metal stents. Modeling and simulation can be used to improve device performance. In this study, a general mathematical model for releasing a hydrophobic drug from a drug-eluting stent, DES, with a biostable coating is modeled. Most mathematical models allow the drug in the polymer to be released freely. This is suitable when the initial concentration of the drug in the polymer is less than the solubility, in which case the dissolution of the drug can be considered instantaneously. On the other hand, matrix devices can be loaded above solubility to provide zero-order release. to this end, we have equipped a model with a function that determines how the dissolution processes change with the dispersed phase discharge. The general model is analyzed with some limitations, and it is reduced to a new model that is consistent with previous studies. We examine the effects of initial drug loading and dissolution rate constant in numerically solving one of the new models, which is novel in DESs.https://jmm.guilan.ac.ir/article_5596_4be60a8e3b3bf76a8908e17fbb89ce0e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201A posteriori error analysis for the Cahn-Hilliard equation437452572610.22124/jmm.2022.22244.1960ENAliMesforushFaculty of Mathematical Sciences, Shahrood University of Thechnology, Shahrood, Iran0000-0001-9098-8953StigLarssonDepartment of Mathematical Sciences, Chalmers University of Technology, Goteborg, Sweden0000-0003-3291-3456Journal Article20220506The Cahn-Hilliard equation is discretized by a Galerkin finite element method based on continuous piecewise linear functions in space and discontinuous piecewise constant functions in time. A posteriori error estimates are proved by using the methodology of dual weighted residuals.https://jmm.guilan.ac.ir/article_5726_bc4d4cc24c04a6629db752a2e511fe45.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201A direct solver for solving systems of linear equations with banded ill-conditioned Toeplitz matrices453461572910.22124/jmm.2022.22278.1965ENNasserAkhoundiSchool of Mathematics and Computer Science, Damghan University, Damghan, IranJournal Article20220511In this paper, the banded Toeplitz matrices generated by $f(\theta)=(2(1-\cos(\theta-\tilde{\theta})))^d$ are studied. The function $f$ is a real non-negative function with a zero of order $2d$ at $\tilde{\theta}$ and the generated matrices are ill-conditioned Hermitian positive definite. We show that these banded Toeplitz matrices are similar to the banded real symmetric positive definite Toeplitz matrices that are generated by $f(\theta)=(2(1-\cos(\theta)))^d$. A fast direct solver is proposed to compute the inverse of these real matrices. Numerical experiments show that our proposed method is faster and more stable than the stable Levinson algorithm.https://jmm.guilan.ac.ir/article_5729_9e8c907b3f56d3cb7dc728d9fd6fe89c.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Stable recovery of a space-dependent force function in a one-dimensional wave equation via Ritz collocation method463480573110.22124/jmm.2022.22186.1956ENKamalRashediDepartment of Mathematics, University of Science and Technology of Mazandaran, Behshahr, MazandaranFatemehBaharifardSchool of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, IranAydinSarrafGlobal Artificial Intelligence Accelerator, Ericsson, Montreal, QC, H4S 0B6, CanadaJournal Article20220427In this paper, we consider the problem of approximating the displacement and the wave sink or source in a 1D wave equation from various measurements. First, the problem is recast as a certain hyperbolic equation. Then, we propose a Ritz approximation as the solution of the reformulated problem and apply the collocation method to convert the inverse problem to a system of linear equations. Since the problem is not well-posed, the numerical discretization of the problem may produce a system of equations that is not well-conditioned. Therefore, we apply the Tikhonov regularization method to obtain a stable solution. For the contaminated measurements, we take advantage of the mollification method in order to derive stable numerical derivatives. Several test examples are provided to show the effectiveness of the proposed technique for obtaining satisfactory results.https://jmm.guilan.ac.ir/article_5731_badac31565469624a3af3584cf4f27b9.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Two efficient heuristic algorithms for the integrated production planning and warehouse layout problem481494573210.22124/jmm.2022.22637.2002ENMohammadPourmohammadi FallahDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranMaziarSalahiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20220708In (Zhang et al. An integrated strategy for a production planning and warehouse layout problem: modeling and solution approaches, Omega 68 (2017) 85--94) the authors have proposed a mixed-integer linear programming model for the integrated production planning and warehouse layout problem. To solve the model, they proposed a Lagrangian relax-and-fix heuristic that takes significant amount of time to stop with gaps above 5$\%$ for large-scale instances. Here, we present two heuristic algorithms to solve the problem. In the first one, we use a greedy approach by allocating warehouse locations with less reservation costs, and also less transportation costs from the production area to locations and from locations to the output point to items with higher demands. Then a smaller model is solved. In the second heuristic, first we sort items in descending order according to the fraction of sum of the demands for that item in the time horizon plus the maximum demand for that item in the time horizon and sum of all its demands in the time horizon. Then we categorize the sorted items into groups of 3, 4, or 5, and solve a small-scale optimization problem for each group, hoping to improve the solution of the first heuristic. Our preliminary numerical results show the effectiveness of the proposed heuristics.https://jmm.guilan.ac.ir/article_5732_e5c4926981a503325f304b440cd3d64d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Improving Canny edge detection algorithm using fractional-order derivatives495514575510.22124/jmm.2022.21875.1921ENMinaMortazaviDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.0000-0001-7444-258XMortazaGachpazanDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran0000-0001-5662-0207MahmoodAmintoosiFaculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran0000-0001-9640-6475Journal Article20220308One of the purposes of edge detection is to use methods that be able to process visual information according to human needs. Therefore, an edge detector is reliable when evaluated by measurement criteria before use in computer vision tools. These criteria compute the difference between the ground truth edge map (reference image) and the original image. In this study, we propose an improved Canny edge detection method based on the fractional-order operators to extract the ideal edge map. Then, by changing the hysteresis thresholds, the thin edges are obtained by filtering gradient calculations based on fractional-order masks. In addition, we employ common fractional-order derivative operators to extract the edge strength and enhance image edge contrast. The plotted curves of the edge detection criteria show that the obtained edge map of the proposed edge detection operator, which is considered to be the minimal rating of measurement, is visually and quantitatively closer to ground truth.https://jmm.guilan.ac.ir/article_5755_2afd3f37da4de5ad303e7d1085999ddc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation515534580310.22124/jmm.2022.21484.1883ENEshetu BeleteDerzieDepartment of Mathematics, Adama Science and Technology University, Adama, Ethiopia0000-0002-8203-8621Justin B.MunyakaziDepartment of Mathematics and Applied Mathematics, University of the Western Cape, Private BagX17, Bellville 7535, South Africa0000-0001-7420-6595Tekle GemechuDinkaDepartment of Mathematics, Adama Science and Technology University, Adama, EthiopiaJournal Article20220108We develop a robust uniformly convergent numerical scheme for singularly perturbed time dependent Burgers-Huxley partial differential equation. We first discretize the time derivative of the equation using the Crank-Nicolson finite difference method. Then, the resulting semi-discretized nonlinear ordinary differential equations are linearized using the quasilinearization technique, and finally, design a fitted operator upwind finite difference method to resolve the layer behavior of the solution in the spatial direction. Our analysis has shown that the presented method is second order parameter uniform convergent in time and first order in space. Numerical experiments are conducted to validate the theoretical results. https://jmm.guilan.ac.ir/article_5803_f77aaacecd347546dc796f1f6f3cf1ae.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201On the solution of parameterized Sylvester matrix equations535553580810.22124/jmm.2022.22153.1950ENMarziehDehghani-MadisehDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20220417In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and so the parameterized system of equations appears. This work considers the parameterized Sylvester matrix equations and tries to propose some methods containing a direct method and two iterative methods to obtain outer estimations of the solution set.https://jmm.guilan.ac.ir/article_5808_22ca8b390e73ed2c3bf93593a7629eae.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201WENO schemes with Z-type non-linear weighting procedure for fractional differential equations555567589210.22124/jmm.2022.22535.1988ENRooholahAbedianSchool of Engineering Science, College of Engineering, University of Tehran, Iran0000-0002-1739-5964Journal Article20220623In this paper, a new fourth-order finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the fractional differential equations which may contain non-smooth solutions at a later time, even if the initial solution is smooth enough. A set of Z-type non-linear weights is constructed based on the $L_1$ norm, yielding improved WENO scheme with more accurate resolution. The Caputo fractional derivative of order $\alpha$ is split into a weakly singular integral and a classical second derivative. The classical Gauss-Jacobi quadrature is employed for solving the weakly singular integral. Also, a new WENO-type reconstruction methodology for approximating the second derivative is developed. Some benchmark examples are prepared to illustrate the efficiency, robustness, and good performance of this new finite difference WENO-Z scheme.https://jmm.guilan.ac.ir/article_5892_31bc383e7160229ae7d3e6280493e694.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10420221201Analysis of $GI/M/1/N$ and $GI/Geo/1/N$ queues with balking and vacation interruptions569585589310.22124/jmm.2022.22579.1996ENKanithiJyothsnaDepartment of Basic Sciences and Humanities, Vignan's Institute of Engineering for Women, Visakhapatnam 530 049, Andhra Pradesh, India0000-0002-3094-3400Vijaya LaxmiPikkalaDepartment of Applied Mathematics, Andhra University, Visakhapatnam 530 003, Andhra Pradesh, IndiaVijaya KumarPrathiDepartment of Mathematics, GITAM (Deemed to be University), Visakhapatnam 530 045, Andhra Pradesh, IndiaJournal Article20220701This paper addresses renewal input continuous and discrete time queues with balking and vacation interruptions. An arriving client may join the system or balk with some state-dependent probability. Whenever the server finds an empty system, he leaves for a working vacation. During working vacations, if there are clients to be served at a service completion instant, the server interrupts the working vacation and switches to regular service period. The embedded Markov chain technique has been adopted for evaluating pre-arrival epoch probabilities and supplementary variable approach is employed to evaluate arbitrary instant probabilities. Few performance characteristics and sojourn time distribution have also been demonstrated. Finally, numerical investigations have been figured out to depict the impact of the model variables on the performance indices.https://jmm.guilan.ac.ir/article_5893_8aca2a3595a9e389e33d78c12e9acc7a.pdf