University of GuilanJournal of Mathematical Modeling2345-394X10220220601An efficient numerical approach for singularly perturbed parabolic convection-diffusion problems with large time-lag173110494010.22124/jmm.2021.19608.1682ENNaolNegeroDepartment of Mathematics, College of Natural Science, Wollega University, Nekemte, Ethiopia0000-0003-1593-735XGemechisDuressaDepartment of Mathematics, College of Natural Science, Jimma University, Jimma, Ethiopia0000-0003-1889-4690Journal Article20210514In this paper, an efficient finite difference method is presented for solving singularly perturbed linear second order parabolic problems with large time lag. The comparable numerical model is related to automatically controlled system with spatial diffusion of reactants in the processes. This study focuses on the formation of boundary layer behavior or oscillatory behaviors due to the presence of delay parameters and perturbation parameter. The numerical scheme comprising an exponentially fitted spline based difference scheme on a uniform mesh supported by Crank-Nicolson Method is constructed. It is found that the present method converges with second order accurate in both temporal and spatial variables. The convergence analysis and running time of the program with varied grid sizes are then used to do the efficiency analysis. The proposed scheme accuracy and efficiency are also demonstrated through numerical experiments.https://jmm.guilan.ac.ir/article_4940_8b2619ee0be1c7e0b77adc160a5daa75.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Existence of positive solutions for a $p$-Laplacian equation with applications to Hematopoiesis191201499810.22124/jmm.2021.19445.1670ENSeshadevPadhiDepartment of Mathematics, Birla Institute of Technology, Mesra, Ranchi, IndiaJaffarAliDepartment of Mathematics, Florida Gulf Coast University FortMyres, Florida, USAAnkurKanaujiyaDepartment of Mathematics, National Institute of Technology Rourkela, IndiaJugalMohapatraDepartment of Mathematics, National Institute of Technology Rourkela, India0000-0001-5118-3933Journal Article20210425This paper is concerned with the existence of at least one positive solution for a boundary value problem (BVP), with $p$-Laplacian, of the form<br /> begin{equation*}<br /> begin{split}<br /> (Phi_p(x^{'}))^{'} + g(t)f(t,x) &= 0, quad t in (0,1),\<br /> x(0)-ax^{'}(0) = alpha[x], & quad<br /> x(1)+bx^{'}(1) = beta[x],<br /> end{split}<br /> end{equation*}<br />where $Phi_{p}(x) = |x|^{p-2}x$ is a one dimensional $p$-Laplacian operator with $p>1, a,b$ are real constants and $alpha,beta$ are the Riemann-Stieltjes integrals<br /> begin{equation*}<br /> begin{split}<br /> alpha[x] = int limits_{0}^{1} x(t)dA(t), quad beta[x] = int limits_{0}^{1} x(t)dB(t),<br /> end{split}<br /> end{equation*}<br />with $A$ and $B$ are functions of bounded variation. A Homotopy version of Krasnosel'skii fixed point theorem is used to prove our results.https://jmm.guilan.ac.ir/article_4998_3322a263b4422e6b70cdc6614aabe9b8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601On the stability functions of second derivative implicit advanced-step point methods203212500010.22124/jmm.2021.20196.1760ENGholamrezaHojjatiFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranLeilaTaheri KoltapeFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20210719In the construction of efficient numerical methods for the stiff initial value problems, some second derivative multistep methods have been introduced equipping with super future point technique. In this paper, we are going to introduce a formula for the stability functions of a class of such methods. This group of methods encompasses SDBDF methods and their extensions with advanced step-point feature. This general formula, instead of obtaining the distinct stability functions for each of methods, will facilitate stability analysis of the methods.https://jmm.guilan.ac.ir/article_5000_f102d35db20a40d0bdb600e319a1e272.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Inverse spectral problems for arrowhead matrices213225501010.22124/jmm.2021.19736.1695ENFeryaFathiDepartment of Mathematics, Dezful Branch, Islamic Azad University, Dezful, IranMohammad AliFariborzi AraghiDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran0000-0002-5467-9296Seyed AbolfazlShahzadeh FazeliDepartment of Computer Science,Yazd University, Yazd, IranJournal Article20210527The 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.https://jmm.guilan.ac.ir/article_5010_61a4d98f5207693ce479fd614d0102dc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601A bargaining game model for performance evaluation in network DEA considering shared inputs in the presence of undesirable outputs227245508210.22124/jmm.2021.19170.1643ENSharifehSoofizadehDepartment of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, IranRezaFallahnejadDepartment of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran0000-0003-3068-0302Journal Article20210329Data Envelopment Analysis (DEA) is a non-parametric method for measuring the relative efficiency of peer decision-making units (DMUs), where the internal structures of DMUs are treated as a black box. Traditional DEA models do not pay attention to the internal structures and intermediate values. Network data envelopment analysis models addressed this shortcoming by considering intermediate measure. The results of two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The centralized model has been widely used to evaluate the efficiency of two-stage systems, but the allocation problem of shared inputs and undesirable outputs has not been considered. The aim of this paper is to develop a method based on bargaining for evaluation in network DEA considering shared inputs and undesirable outputs. The two stages are considered as players to bargain for a better payoff, which is offered by DEA ratio efficiency score of DMUs. The efficiency model is developed as a cooperative game model. Finally, a numerical example is given to evaluate the proposed model.https://jmm.guilan.ac.ir/article_5082_8ffa7b7c182161e54ac3e18d08a67c9a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Local discontinuous Galerkin method for the numerical solution of fractional compartmental model with application in pharmacokinetics247261508510.22124/jmm.2021.20561.1790ENHadiMohammadi-FirouzjaeiDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran0000-0002-7018-500XMonaAdibiDepartment of Health, Safety and Environment (Department of Health)
Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, IranHojatollahAdibiDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, IranJournal Article20210910This paper provides a numerical solution for the fractional multi-compartmental models which are applied in pharmacokinetics. We implement the local discontinuous Galerkin method for these fractional models with the upwind numerical fluxes. To obtain high-order results with adequate accuracy, the third-order approximation polynomials are used. Finally, to validate the scheme, the results are compared with the solutions of a semi-analytical method.https://jmm.guilan.ac.ir/article_5085_58a41872757ce24339bd2ed281ccafb4.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Accurate and fast matrix factorization for low-rank learning263278508610.22124/jmm.2021.19892.1723ENRezaGodazDepartment of Computer Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, IranRezaMonsefiDepartment of Computer Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, IranFaezehToutounianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranReshadHosseiniDepartment of Electrical and Computer Engineering, University of Tehran, Tehran, IranJournal Article20210615In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan bidiagonalization (GK-bidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two different image datasets of MNIST and USPS.https://jmm.guilan.ac.ir/article_5086_1eba2b613af075da409d2bffc34e4d52.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601A new fifth-order symmetrical WENO-Z scheme for solving Hamilton-Jacobi equations279297516410.22124/jmm.2021.20251.1765ENRooholahAbedianDepartment of engineering science, College of engineering, University of Tehran, Tehran, Iran0000-0002-1739-5964Journal Article20210729This research describes a new fifth-order finite difference symmetrical WENO-Z scheme for solving Hamilton-Jacobi equations. This method employs the same six-point stencil as the original fifth-order WENO scheme (SIAM J. Sci. Comput. 21 (2000) 2126--2143) and a new WENO scheme recently proposed (Numer. Methods Partial Differential Eq. 33 (2017) 1095--1113), and could generate better results and create the same order of accuracy in smooth area without loss of accuracy at critical points simultaneously avoiding incorrect oscillations in the vicinity of the singularities. The new reconstruction is a convex combination of a fifth-order linear reconstruction and three third-order linear reconstructions. We prepare a detailed analysis of the approximation order of the designed WENO scheme. Some benchmark tests in 1D, 2D and 3D are performed to display the capability of the scheme.https://jmm.guilan.ac.ir/article_5164_25a1f32cba9f1942480294f3131b9a4d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601An efficient wavelet-based numerical method to solve nonlinear Fredholm integral equation of second kind with smooth kernel299313516810.22124/jmm.2021.20512.1785ENJyotirmoyMouleyDepartment of Applied Mathematics, University of Calcutta, Kolkata, India0000-0001-8353-0813Birendra NathMandalPhysics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, IndiaJournal Article20210904In this paper, a wavelet-based numerical algorithm is described to obtain approximate numerical solution of a class of nonlinear Fredholm integral equations of second kind having smooth kernels. The algorithm involves approximation of the unknown function in terms of Daubechies scale functions. The properties of Daubechies scale and wavelet functions together with one-point quadrature rule for the product of a smooth function and Daubechies scale functions are utilized to transform the integral equation to a system of nonlinear equations. The efficiency of the proposed method is demonstrated through three illustrative examples.https://jmm.guilan.ac.ir/article_5168_a82fb0f8389eb98e7575121f1d06f1bb.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Combination of Sinc and radial basis functions for time-space fractional diffusion equations315329521810.22124/jmm.2021.17929.1546ENSolmazMohammadi RickDepartment of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, IranRashidiniaJalilSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 168613114, Iran0000-0002-9177-900xAmir HoseinRefahi SheikhaniDepartment of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, IranJournal Article20201014We study the combination of the Sinc and the Gaussian radial basis functions (GRBF) to develop the numerical methods for the time--space fractional diffusion equations with the Riesz fractional derivative. The GRBF is used to approximate the unknown function in spatial direction and the Sinc quadrature rule associated with double exponential transformation is applied to approximate the arising integrals. Three practical examples are considered for testing the ability of the proposed method. https://jmm.guilan.ac.ir/article_5218_81ea39064c5dfdcd5ac7655e5527a700.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Study on the stability for implicit second-order differential equation via integral boundary conditions331348523110.22124/jmm.2021.19931.1725ENAhmed Mohamed AhmedEl-SayedDepartment of Mathematics, Alexandria University, Alexandria, Egypt0000-0001-7092-7950Hind Hassan GaberHashemDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644 Buraidah 51452, Saudi ArabiaShorouk MahmoudAl-IssaDepartment of Mathematics, The International University of Beirut, Beirut, Lebanonhttps://orcid.org/00Journal Article20210620In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit second-order differential equations are investigated via fractional-orders integral boundary conditions by direct application of the Banach contraction principle. Finally, we present some particular cases and two examples to illustrate our results.https://jmm.guilan.ac.ir/article_5231_103a07a6c5ffdae71942c28dcdb8c475.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X10220220601Numerical solutions of system of two-dimensional Volterra integral equations via operational matrices of hybrid functions349365523410.22124/jmm.2021.19962.1727ENKhosrowMaleknejadSchool of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, IranMaryamShahabiSchool of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, IranJournal Article20210624The main target of this paper is to solve a system of two-dimensional Volterra integral equations (2-DVIEs). Operational Matrices of two-dimensional hybrid of block-pulse functions and Legendre polynomials are applied to reduce these systems of integral equations to a system of algebraic equations. The main benefit of these basic functions is their efficiency in dealing with non-sufficiently smooth functions. An error bound is provided and some examples are prepared to verify the applicability of the offered numerical technique.https://jmm.guilan.ac.ir/article_5234_42c175bee102a6b0ba16febc2bf5d02a.pdf