2024-03-28T13:46:06Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=679
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
$2n$-by-$2n$ circulant preconditioner for a kind of spatial fractional diffusion equations
Naser
Akhoundi
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
2020
06
01
207
218
https://jmm.guilan.ac.ir/article_4013_fe2cb10372a1363c89f327e7cdd86bc4.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
Numerical study of optimal control domain decomposition for nonlinear boundary heat in the human eye
Salem
Ahmedou bamba
Abdellatif
Ellabib
Abdessamad
El madkouri
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
2020
06
01
219
240
https://jmm.guilan.ac.ir/article_4014_a0676ec363b476312dc79735f2b6be28.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
Vehicular traffic models for speed-density-flow relationship
Gabriel
Fosu
Emmanuel
Akweittey
Joseph M.
Opong
Micheal E.
Otoo
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
2020
06
01
241
255
https://jmm.guilan.ac.ir/article_4015_3934c2b0789ac8b8eda2a5391be4b890.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
Ulam stabilities for nonlinear fractional integro--differential equations with constant coefficient via Pachpatte's inequality
Shivaji Ramchandra
Tate
Hambirrao Tatyasaheb
Dinde
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
2020
06
01
257
278
https://jmm.guilan.ac.ir/article_4026_910843d75a47e8ac970737639bf5d7f1.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
A simulated annealing algorithm for the restricted stochastic traveling salesman problem with exponentially distributed arc lengths
Mohsen
Abdolhosseinzadeh
Mir Mohammad
Alipour
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
2020
06
01
279
290
https://jmm.guilan.ac.ir/article_4027_7430873ed63a7620715be6db6623dc1b.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
The method of lines for parabolic integro-differential equations
Samaneh
Soradi Zeid
Mehdi
Mesrizadeh
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
2020
06
01
291
308
https://jmm.guilan.ac.ir/article_4037_6fc65daf4904bd5ada4c05abbf37e869.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
3
A survey on compressive sensing: classical results and recent advancements
Ahmad
Mousavi
Mehdi
Rezaee
Ramin
Ayanzadeh
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
2020
06
01
309
344
https://jmm.guilan.ac.ir/article_4155_b84c66cd66053821ec4e8c2447fd3bf1.pdf