University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
$2n$-by-$2n$ circulant preconditioner for a kind of spatial fractional diffusion equations
207
218
EN
Naser
Akhoundi
School of mathematics and computer science, Damghan university, Damghan, Iran
akhoundi@du.ac.ir
10.22124/jmm.2020.15908.1391
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.
Fractional diffusion equation,circulant matrix,skew-circulant matrix,Toeplitz matrix,Krylov subspace methods
https://jmm.guilan.ac.ir/article_4013.html
https://jmm.guilan.ac.ir/article_4013_fe2cb10372a1363c89f327e7cdd86bc4.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
Numerical study of optimal control domain decomposition for nonlinear boundary heat in the human eye
219
240
EN
Salem
Ahmedou bamba
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
salemmohamed39@gmail.com
Abdellatif
Ellabib
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
a.ellabib@uca.ac.ma
Abdessamad
El madkouri
Universite' Cadi Ayyad, Faculte' des Sciences et Techniques, Marrakech, Maroc
abdessamad.elmadkouri@edu.uca.ma
10.22124/jmm.2020.15163.1363
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.
Heat distribution,human eye,optimal control,Dirichlet-Neumann,boundary element method
https://jmm.guilan.ac.ir/article_4014.html
https://jmm.guilan.ac.ir/article_4014_a0676ec363b476312dc79735f2b6be28.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
Vehicular traffic models for speed-density-flow relationship
241
255
EN
Gabriel
O.
Fosu
0000-0001-9906-2970
Department of Mathematics, Presbyterian University College, Ghana
gabriel.obed@presbyuniversity.edu.gh
Emmanuel
Akweittey
Department of Mathematics, Presbyterian University College, Ghana
emmanuel.akweittey@presbyuniversity.edu.gh
Joseph M.
Opong
Department of Mathematics, Presbyterian University College, Ghana
joeopong@presbyuniversity.edu.gh
Micheal E.
Otoo
Department of Mathematics, Presbyterian University College, Ghana
moezra@presbyuniversity.edu.gh
10.22124/jmm.2020.15409.1370
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.
LWR model,shockwaves,speed-density equation,traffic flow
https://jmm.guilan.ac.ir/article_4015.html
https://jmm.guilan.ac.ir/article_4015_3934c2b0789ac8b8eda2a5391be4b890.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
Ulam stabilities for nonlinear fractional integro--differential equations with constant coefficient via Pachpatte's inequality
257
278
EN
Shivaji Ramchandra
Tate
0000-0002-0323-7308
Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, India
tateshivaji@gmail.com
Hambirrao Tatyasaheb
Dinde
Department of Mathematics, Karmaveer Bhaurao Patil College, Urun--Islampur, India
drhtdmaths@gmail.com
10.22124/jmm.2020.15923.1392
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.
Boundary value conditions,Caputo's fractional derivative,Fixed point,integral inequality,Stability
https://jmm.guilan.ac.ir/article_4026.html
https://jmm.guilan.ac.ir/article_4026_910843d75a47e8ac970737639bf5d7f1.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
A simulated annealing algorithm for the restricted stochastic traveling salesman problem with exponentially distributed arc lengths
279
290
EN
Mohsen
Abdolhosseinzadeh
0000-0002-5922-6659
Department of Mathematics, University of Bonab, Bonab, Iran
mohsen.ab@ubonab.ac.ir
Mir Mohammad
Alipour
Department of Computer Engineering, University of Bonab, Bonab, Iran
alipour@ubonab.ac.ir
10.22124/jmm.2020.15535.1378
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.
Travelling salesman problem,discrete time Markov chain,approximation algorithms,Simulated Annealing
https://jmm.guilan.ac.ir/article_4027.html
https://jmm.guilan.ac.ir/article_4027_7430873ed63a7620715be6db6623dc1b.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
The method of lines for parabolic integro-differential equations
291
308
EN
Samaneh
Soradi Zeid
Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran
soradizeid@eng.usb.ac.ir
Mehdi
Mesrizadeh
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
m.mesrizadeh@yahoo.com
10.22124/jmm.2020.15954.1397
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.
Parabolic integro-differential equation,partial differential equation,meshless method,radial point interpolation technique,group preserving scheme
https://jmm.guilan.ac.ir/article_4037.html
https://jmm.guilan.ac.ir/article_4037_6fc65daf4904bd5ada4c05abbf37e869.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
8
3
2020
06
01
A survey on compressive sensing: classical results and recent advancements
309
344
EN
Ahmad
Mousavi
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, USA
amousavi@umn.edu
Mehdi
Rezaee
Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA
rezaee1@umbc.edu
Ramin
Ayanzadeh
Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA
ayanzadeh@umbc.edu
10.22124/jmm.2020.16701.1450
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.
compressive sensing,$ell_p$ recovery,greedy algorithms
https://jmm.guilan.ac.ir/article_4155.html
https://jmm.guilan.ac.ir/article_4155_b84c66cd66053821ec4e8c2447fd3bf1.pdf