2020
8
1
0
0
1

A modified conjugate gradient method based on a modified secant equation
https://jmm.guilan.ac.ir/article_3760.html
10.22124/jmm.2019.14807.1343
1
QuasiNewton 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 quasiNewton 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.
0

1
20


Parvaneh
Faramarzi
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran
Iran
faramarzi.parvaneh@razi.ac.ir


Keyvan
Amini
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran
Iran
kamini@razi.ac.ir
Conjugate gradient methods
Modified secant condition
Sufficient descent condition
Global convergence
1

New nonlinear conjugate gradient methods based on optimal DaiLiao parameters
https://jmm.guilan.ac.ir/article_3761.html
10.22124/jmm.2019.14737.1338
1
Here, three new nonlinear conjugate gradient (NCG) methods are proposed, based on a modified secant equation introduced in (IMA. J. Num. Anal. 11 (1991) 325332) and optimal DaiLiao (DL) parameters (Appl. Math. Optim. 43 (2001) 87101). 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 quasinewton 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 wellknown methods.
0

21
39


Saeed
Nezhadhosein
Department of Mathematics, Payame Noor University, Tehran 193953697, Iran
Iran
s_nejhadhosein@pnu.ac.ir
Unconstrained optimization
Modified secant equations
DaiLiao conjugate gradient method
1

A macroscopic second order model for air traffic flow
https://jmm.guilan.ac.ir/article_3787.html
10.22124/jmm.2019.15035.1359
1
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 LighthillWhithamRichards 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.
0

41
54


Mahboobeh
Hoshyar Sadeghian
Department of Applied Mathematics, Faculty of Mathematical Science,
Ferdowsi University of Mashhad, Mashhad, Iran
Iran
ma_hs987@mail.um.ac.ir


Mortaza
Gachpazan
Department of Applied Mathematics, Faculty of Mathematical Science,
Ferdowsi University of Mashhad, Mashhad, Iran
Iran
gachpazan@um.ac.ir


Nooshin
Davoodi
Department of Applied Mathematics, Faculty of Mathematical Science,
Ferdowsi University of Mashhad, Mashhad, Iran
Iran
davoodi.math@gmail.com


Faezeh
Toutounian
Department of Applied Mathematics, Faculty of Mathematical Science,
Ferdowsi University of Mashhad, Mashhad, Iran
Iran
toutouni@um.ac.ir
Air traffic flow
macroscopic model
LWR model
Newton's second law
upwind scheme
1

A fitted mesh method for a coupled system of two singularly perturbed first order differential equations with discontinuous source term
https://jmm.guilan.ac.ir/article_3875.html
10.22124/jmm.2020.12824.1245
1
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, piecewiseuniform 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.
0

55
70


Sheetal
Chawla
Department of Mathematics, Pt. N.R.S. Government College Rohtak, Haryana124001, India
Iran
chawlaasheetal@gmail.com


Urmil
Suhag
Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana124001, India
Iran
urmilsuhag@gmail.com


Jagbir
Singh
Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana124001, India
Iran
ahlawatjagbir@gmail.com
Singular perturbation
parameteruniform convergence
backward difference scheme
Shishkin mesh
Bakhvalov mesh
initial and interior layers
1

The evolution of the free boundary separating two immiscible viscous fluids in an elastic porous medium
https://jmm.guilan.ac.ir/article_3876.html
10.22124/jmm.2020.14831.1349
1
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.
0

71
90


Oleg Vladimirovich
Galtsev
Department of Information and Robotic Systems, Belgorod State National Research University, Belgorod, Russia
Iran
oleg_galtsev@mail.ru
Hydrodynamic modeling
fluid flows
fluidstructure interaction
1

Cellular automaton model for substitutional binary diffusion in solids
https://jmm.guilan.ac.ir/article_3877.html
10.22124/jmm.2020.13012.1255
1
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 [condmat.statmech]) that exhibits the Kirkendall effect. The framework allows the exploration of other state change rules based on additional physical mechanisms.
0

91
104


Helena
Ribera
Centre de Recerca Matematica, Campus de Bellaterra, Spain
Iran
heleribera@gmail.com


Brian T. R.
Wetton
Mathematics Department, University of British Columbia, Canada
Iran
wetton@math.ubc.ca


Timothy
Myers
Centre de Recerca Matematica, Campus de Bellaterra, Spain
Iran
tim.myerscrm@gmail.com
Kirkendall effect
Diffusion
Hollow nanostructures
Cellular automaton