University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 A modified conjugate gradient method based on a modified secant equation 1 20 3760 10.22124/jmm.2019.14807.1343 EN Parvaneh Faramarzi Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran Keyvan Amini Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran 0000-0002-9264-3091 Journal Article 2019 10 22 Quasi-Newton methods are one of the popular iterative schemes to solve unconstrained optimization problems. The high convergence rate and excellent precision are two prominent characteristics of the quasi-Newton methods. In this paper, according to the preferable properties of a modified secant condition, a modified conjugate gradient method is introduced. The new algorithm satisfies the sufficient descent property independent of the line search. The convergence properties of the proposed algorithm are investigated both for uniformly convex and general functions. Numerical experiments show the superiority of the proposed method.<br /><br />
University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters 21 39 3761 10.22124/jmm.2019.14737.1338 EN Saeed Nezhadhosein Department of Mathematics, Payame Noor University, Tehran 193953697, Iran Journal Article 2019 10 15 Here, three new nonlinear conjugate gradient (NCG) methods are proposed,  based on a modified secant equation introduced in (IMA. J.  Num.  Anal. 11 (1991) 325-332) and optimal Dai-Liao (DL) parameters (Appl.  Math.  Optim.  43 (2001) 87-101). Firstly, an extended conjugacy condition is obtained,  which leads to a new DL parameter. Next, to set this parameter,   we use three approaches such that the search directions be close to some descent or quasi-newton directions. Global convergence of the proposed methods for uniformly convex functions and general functions is proved.   Numerical experiments are done on  a set of test functions of the CUTEr collection and the results of these NCGs are compared with some well-known methods.
University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 A macroscopic second order model for air traffic flow 41 54 3787 10.22124/jmm.2019.15035.1359 EN Mahboobeh Hoshyar Sadeghian Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran Mortaza Gachpazan Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran 0000-0001-5662-0207 Nooshin Davoodi Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran Faezeh Toutounian Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran Journal Article 2019 11 27 In this paper,  we introduce a new dynamic model for the air traffic flow prediction to estimate the traffic distribution for given airspaces in the future.  Based on Lighthill-Whitham-Richards traffic flow model and the Newton's second law,  we establish a nonlinear model to describe interrelationship and influential factors of the three characteristic parameters as traffic flow, density,  and velocity.  The upwind scheme is applied to perform the numerical simulations. Numerical results show that the proposed model can reproduce the evolution of shockwave, rarefaction wave,  and small perturbation.
University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 A fitted mesh method for a coupled system of two singularly perturbed first order differential equations with discontinuous source term 55 70 3875 10.22124/jmm.2020.12824.1245 EN Sheetal Chawla Department of Mathematics, Pt. N.R.S. Government College Rohtak, Haryana-124001, India Urmil Suhag Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana-124001, India Jagbir Singh Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana-124001, India Journal Article 2019 03 14 In this work, an initial value problem for a weakly coupled system of two singularly perturbed ordinary differential equations with discontinuous source term is considered. In general, the system does not obey the standard maximum principle. The solution to the system has initial and  interior layers that overlap and interact. To analyze the behavior of these layers, piecewise-uniform Shishkin meshes and graded Bakhvalov meshes are constructed. A backward finite difference scheme is considered on the meshes and is proved to be  uniformly convergent in the maximum norm. Numerical experiments for both the Shishkin and Bakhvalov meshes are provided in support of the theory.
University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 The evolution of the free boundary separating two immiscible viscous fluids in an elastic porous medium 71 90 3876 10.22124/jmm.2020.14831.1349 EN Oleg Vladimirovich Galtsev Department of Information and Robotic Systems, Belgorod State National Research University, Belgorod, Russia 0000-0001-7786-4294 Journal Article 2019 10 31 We consider the evolution of the free boundary separating two immiscible viscous fluids with different constant densities in an elastic porous skeleton. The motion of the liquids is described by the Stokes equations driven by the input pressure and the force of gravity. For flows in a bounded domain, we emphasize the study of the properties of the moving boundary separating the two fluids.
University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 Cellular automaton model for substitutional binary diffusion in solids 91 104 3877 10.22124/jmm.2020.13012.1255 EN Helena Ribera Centre de Recerca Matematica, Campus de Bellaterra, Spain Brian T. R. Wetton Mathematics Department, University of British Columbia, Canada 0000-0002-6808-6301 Timothy Myers Centre de Recerca Matematica, Campus de Bellaterra, Spain Journal Article 2019 04 15 We use the cellular automaton (CA) approach to model  binary diffusion in solids. We define an asynchronous CA model and formally take its continuum limit and show it approaches a  differential equation model derived in previous work (Ribera, Wetton, and Myers, 2019, arXiv:1911.07359 [cond-mat.stat-mech]) that exhibits the Kirkendall effect. The framework allows the exploration of other state change rules based on additional physical mechanisms.