ORIGINAL_ARTICLE
$2n$-by-$2n$ circulant preconditioner for a kind of spatial fractional diffusion equations
In this paper, a $2n$-by-$2n$ circulant preconditioner is introduced for a system of linear equations arising from discretization of the spatial fractional diffusion equations (FDEs). We show that the eigenvalues of our preconditioned system are clustered around 1, even if the diffusion coefficients of FDEs are not constants. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient.
https://jmm.guilan.ac.ir/article_4013_fe2cb10372a1363c89f327e7cdd86bc4.pdf
2020-06-01
207
218
10.22124/jmm.2020.15908.1391
Fractional diffusion equation
circulant matrix
skew-circulant matrix
Toeplitz matrix
Krylov subspace methods
Naser
Akhoundi
akhoundi@du.ac.ir
1
School of mathematics and computer science, Damghan university, Damghan, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Numerical study of optimal control domain decomposition for nonlinear boundary heat in the human eye
The present work sheds new light on the computation of the heat distribution on the boundary of the human eye. Due to different values of the thermal conductivity on each region of the human eye, the domain decomposition technique is introduced and an optimization formulation is analysed and studied to derive a proposed algorithm. All obtained partial differential equations are approached by discontinuous dual reciprocity boundary element method. The validity of the proposed approaches is confirmed by comparing to results reported with previous experimental and numerical studies.
https://jmm.guilan.ac.ir/article_4014_a0676ec363b476312dc79735f2b6be28.pdf
2020-06-01
219
240
10.22124/jmm.2020.15163.1363
Heat distribution
human eye
optimal control
Dirichlet-Neumann
boundary element method
Salem
Ahmedou bamba
salemmohamed39@gmail.com
1
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
LEAD_AUTHOR
Abdellatif
Ellabib
a.ellabib@uca.ac.ma
2
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
AUTHOR
Abdessamad
El madkouri
abdessamad.elmadkouri@edu.uca.ma
3
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
AUTHOR
ORIGINAL_ARTICLE
Vehicular traffic models for speed-density-flow relationship
The relationship among vehicles on the road is modeled using fundamental traffic equations. In traffic modeling, a particular speed-density equation usually fits a peculiar dataset. The study seeks to parameterize some existing fundamental models so that a given equation could match different dataset. The new equations are surmisal offshoots from existing equations. The parameterized equations are used in the LWR model and solved using the Lax-Friedrichs differencing scheme. The simulation results illustrate different scenarios of acceleration and deceleration traffic wave profiles. The proposed models appropriately explain the varying transitions of different traffic regimes.
https://jmm.guilan.ac.ir/article_4015_3934c2b0789ac8b8eda2a5391be4b890.pdf
2020-06-01
241
255
10.22124/jmm.2020.15409.1370
LWR model
shockwaves
speed-density equation
traffic flow
Gabriel
Fosu
gabriel.obed@presbyuniversity.edu.gh
1
Department of Mathematics, Presbyterian University College, Ghana
LEAD_AUTHOR
Emmanuel
Akweittey
emmanuel.akweittey@presbyuniversity.edu.gh
2
Department of Mathematics, Presbyterian University College, Ghana
AUTHOR
Joseph M.
Opong
joeopong@presbyuniversity.edu.gh
3
Department of Mathematics, Presbyterian University College, Ghana
AUTHOR
Micheal E.
Otoo
moezra@presbyuniversity.edu.gh
4
Department of Mathematics, Presbyterian University College, Ghana
AUTHOR
ORIGINAL_ARTICLE
Ulam stabilities for nonlinear fractional integro--differential equations with constant coefficient via Pachpatte's inequality
In this article, we study some existence, uniqueness and Ulam type stability results for a class of boundary value problem for nonlinear fractional integro--differential equations with positive constant coefficient involving the Caputo fractional derivative. The main tools used in our analysis is based on Banach contraction principle, Schaefer's fixed point theorem and Pachpatte's integral inequality. Finally, results are illustrated with suitable example.
https://jmm.guilan.ac.ir/article_4026_910843d75a47e8ac970737639bf5d7f1.pdf
2020-06-01
257
278
10.22124/jmm.2020.15923.1392
Boundary value conditions
Caputo's fractional derivative
Fixed point
integral inequality
Stability
Shivaji Ramchandra
Tate
tateshivaji@gmail.com
1
Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, India
LEAD_AUTHOR
Hambirrao Tatyasaheb
Dinde
drhtdmaths@gmail.com
2
Department of Mathematics, Karmaveer Bhaurao Patil College, Urun--Islampur, India
AUTHOR
ORIGINAL_ARTICLE
A simulated annealing algorithm for the restricted stochastic traveling salesman problem with exponentially distributed arc lengths
The considered stochastic travelling salesman problem is defined where the costs are distributed exponentially. The costs are symmetric and they satisfy the triangular inequality. A discrete time Markov chain is established in some periods of time. A stochastic tour is created in a dynamic recursive way and the best node is detected to traverse in each period. Then, a simulated annealing based heuristic method is applied to select the best state. All the nodes should be traversed exactly once. An initial $\rho$-approximate solution is applied for some benchmark problems and the obtained solutions are improved by a simulated annealing heuristic method.
https://jmm.guilan.ac.ir/article_4027_7430873ed63a7620715be6db6623dc1b.pdf
2020-06-01
279
290
10.22124/jmm.2020.15535.1378
Travelling salesman problem
discrete time Markov chain
approximation algorithms
Simulated Annealing
Mohsen
Abdolhosseinzadeh
mohsen.ab@ubonab.ac.ir
1
Department of Mathematics, University of Bonab, Bonab, Iran
LEAD_AUTHOR
Mir Mohammad
Alipour
alipour@ubonab.ac.ir
2
Department of Computer Engineering, University of Bonab, Bonab, Iran
AUTHOR
ORIGINAL_ARTICLE
The method of lines for parabolic integro-differential equations
This paper introduces an efficient numerical scheme for solving a significant class of nonlinear parabolic integro-differential equations (PIDEs). The major contributions made in this paper are applying a direct approach based on a combination of group preserving scheme (GPS) and spectral meshless radial point interpolation (SMRPI) method to transcribe the partial differential problem under study into a system of ordinary differential equations (ODEs). The resulting problem is then solved by employing the numerical method of lines, which is also a well-developed numerical method. Two numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.
https://jmm.guilan.ac.ir/article_4037_6fc65daf4904bd5ada4c05abbf37e869.pdf
2020-06-01
291
308
10.22124/jmm.2020.15954.1397
Parabolic integro-differential equation
partial differential equation
meshless method
radial point interpolation technique
group preserving scheme
Samaneh
Soradi Zeid
soradizeid@eng.usb.ac.ir
1
Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran
LEAD_AUTHOR
Mehdi
Mesrizadeh
m.mesrizadeh@yahoo.com
2
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
AUTHOR
ORIGINAL_ARTICLE
A survey on compressive sensing: classical results and recent advancements
Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a successful recovery. This topic is well-nourished and numerous results are available in the literature. However, their dispersity makes it time-consuming for practitioners to quickly grasp its main ideas and classical algorithms, and further touch upon the recent advancements. In this survey, we overview vital classical tools and algorithms in compressive sensing and describe its significant recent advancements. We conclude by a numerical comparison of the performance of described approaches.
https://jmm.guilan.ac.ir/article_4155_b84c66cd66053821ec4e8c2447fd3bf1.pdf
2020-06-01
309
344
10.22124/jmm.2020.16701.1450
compressive sensing
$ell_p$ recovery
greedy algorithms
Ahmad
Mousavi
amousavi@umn.edu
1
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, USA
LEAD_AUTHOR
Mehdi
Rezaee
rezaee1@umbc.edu
2
Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA
AUTHOR
Ramin
Ayanzadeh
ayanzadeh@umbc.edu
3
Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA
AUTHOR