University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
A moving kriging interpolation-based meshfree method for solving two-phase elasticity system
1
12
EN
Ameneh
Taleei
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
a.taleei@sutech.ac.ir
10.22124/jmm.2020.17088.1484
The elasticity interface problems occur frequently when two or more materials meet. In this paper, a meshfree point collocation method based on moving kriging interpolation is proposed for solving the two-phase elasticity system with an arbitrary interface. The moving kriging shape function and its derivatives are constructed by moving kriging interpolation technique. Since the shape function possesses the Kronecker delta property then the Dirichlet boundary condition can be implemented directly and easily. Numerical results demonstrate the accuracy and efficiency of the proposed method for the studied problems with constant and variable coefficients.
Two-phase elasticity system,meshfree method,moving kriging interpolation (MKI),interface problems
https://jmm.guilan.ac.ir/article_4186.html
https://jmm.guilan.ac.ir/article_4186_40f9b084970d75853cfa5b94d6b8ee6a.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
A combined dictionary learning and TV model for image restoration with convergence analysis
13
30
EN
Souad
Mohaoui
Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco
souad.mohaoui@ced.uca.ma
Abdelilah
Hakim
Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco
a.hakim@uca.ma
Said
Raghay
Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco
s.raghay@uca.ma
10.22124/jmm.2020.15408.1369
We consider in this paper the $l_0$-norm based dictionary learning approach combined with total variation regularization for the image restoration problem. It is formulated as a nonconvex nonsmooth optimization problem. Despite that this image restoration model has been proposed in many works, it remains important to ensure that the considered minimization method satisfies the global convergence property, which is the main objective of this work. Therefore, we employ the proximal alternating linearized minimization method whereby we demonstrate the global convergence of the generated sequence to a critical point. The results of several experiments demonstrate the performance of the proposed algorithm for image restoration.
Image deblurring,dictionary learning,sparse approximation,total variation,proximal methods,nonconvex optimization
https://jmm.guilan.ac.ir/article_4187.html
https://jmm.guilan.ac.ir/article_4187_8d48376485cc61654259b0f2dd2b02e0.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Lower bound approximation of nonlinear basket option with jump-diffusion
31
44
EN
Yasser
Taherinasab
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
yassertaherinasab@gmail.com
Ali Reza
Soheili
0000000269905401
Department of applied mathematics
Ferdowsi university of Mashhad
Mashhad and The Center of Excellence on Modeling and Control Systems, Ferdowsi University of Mashhad, Iran
soheili@um.ac.ir
Mohammad
Amini
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran
m-amini@um.ac.ir
10.22124/jmm.2020.16126.1408
We extend the method presented by Xu and Zheng (Int. J. Theor. Appl. Finance 17 (2014) 21--36) for the general case. We develop a numerical-analytic formula for pricing nonlinear basket options with jump-diffusion model. We derive an easily computed method by using the asymptotic expansion to find the approximate value of the lower bound of nonlinear European basket call prices since a nonlinear basket option is generally not closed-form. We use Split Step Backward Euler and Compensated Split Step Backward Euler methods with Monte Carlo simulation to check the validity of the presented method.<br /><br />
Basket option,nonlinear stochastic differential equations,Poisson process,Split Step Backward Euler method
https://jmm.guilan.ac.ir/article_4226.html
https://jmm.guilan.ac.ir/article_4226_1b4d910cad60b8833e6f28bc1332a38b.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Almost periodic positive solutions for a time-delayed SIR epidemic model with saturated treatment on time scales
45
60
EN
Kapula Rajendra
Prasad
College of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003
rajendra92@rediffmail.com
Mahammad
Khuddush
0000-0002-1236-8334
College of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003
khuddush89@gmail.com
Kuparala Venkata
Vidyasagar
College of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003 and Department of Mathematics, Government Degree College for Women, Marripalem, Koyyuru Mandal, Visakhapatnam, India-531116
vidyavijaya08@gmail.com
10.22124/jmm.2020.16271.1420
In this paper, we study a non-autonomous time-delayed SIR epidemic model which involves almost periodic incidence rate and saturated treatment function on time scales. By utilizing some dynamic inequalities on time scales, sufficient conditions are derived for the permanence of the SIR epidemic model and we also obtain the existence and uniform asymptotic stability of almost periodic positive solutions for the addressed SIR model by Lyapunov functional method. Finally numerical simulations are given to demonstrate our theoretical results.
SIR model,time scale,almost periodic incidence rate,almost periodic positive solution,permanence,uniform asymptotic stability
https://jmm.guilan.ac.ir/article_4230.html
https://jmm.guilan.ac.ir/article_4230_9b40bcb9a3cfdf4fe20b7bb07b5f0e64.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Solving the Basset equation via Chebyshev collocation and LDG methods
61
79
EN
Mohammad
Izadi
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
izadi@uk.ac.ir
Mehdi
Afshar
Department of Mathematics and Statistics, Zanjan Branch , Islamic Azad University, Zanjan, Iran.
mafshar@iauz.ac.ir
10.22124/jmm.2020.17135.1489
Two different numerical methods are developed to find approximate solutions of a class of linear fractional differential equations (LFDEs) appearing in the study of the generalized Basset force, when a sphere sinks in a viscous fluid. In the first one, using the Chebyshev bases, the collocation points, and the matrix operations, the given LFDE reduces to a matrix equation while in the second one, we employ the local discontinuous Galerkin (LDG) method, which uses the natural upwind flux yielding a stable discretization. Unlike the first method, in the latter method we are able to solve the problem element by element locally and there is no need to solve a full global matrix. The efficiency of the proposed algorithms are shown via some numerical examples.
Basset equation,Caputo fractional derivative,Chebyshev polynomials,collocation method,Local discontinuous Galerkin method,Numerical stability
https://jmm.guilan.ac.ir/article_4231.html
https://jmm.guilan.ac.ir/article_4231_c43909580b688d457545bf3290f7da3e.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
An RBF approach for oil futures pricing under the jump-diffusion model
81
92
EN
Mohammad
Karimnejad Esfahani
Department of Mathematics, Allameh Tabataba'i University, Iran
mohammad7394@gmail.com
Abdolsadeh
Neisy
Department of Mathematics, Allameh Tabataba'i University, Iran
a_neisy@atu.ac.ir
Stefano
De Marchi
Department of Mathematics "Tullio Levi-Civita", University of Padova, Italy
demarchi@math.unipd.it
10.22124/jmm.2020.15948.1396
In this paper, our concern is to present and solve the problem of pricing oil futures. For this purpose, firstly we suggest a model based on the well-known Schwartz's model, in which the oil futures price is based on spot price of oil and convenience yield, however, the main difference here is that we have assumed that the former was imposed to some jumps, thus we added a jump term to the model of spot price. In our case, the oil future price model would be a Partial Integral Differential Equation (PIDE). Since, no closed form solution can be suggested for these kind of equations, we desire to solve our model with an appropriate numerical method. Although Finite Differences (FD) or Finite Elements (FE) is a common method for doing so, in this paper, we propose an alternative method based on Radial Basis Functions (RBF).
Oil derivative market,Radial Basis Functions (RBF),Oil futures,initial and boundary value problems,jump-diffusion model
https://jmm.guilan.ac.ir/article_4234.html
https://jmm.guilan.ac.ir/article_4234_4601c4bfd9ea42954940b31531be8371.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Caputo-Hadamard fractional differential equation with impulsive boundary conditions
93
106
EN
Ankit
Kumar
Nain
Department of Mathematics and Scientific Computing,
National Institute of Technology, Hamirpur, HP-177005, India
ankitnain744@gmail.com
Ramesh
Kumar
Vats
Department of Mathematics and Scientific Computing,
National Institute of Technology, Hamirpur, HP-177005, India
rameshnitham@gmail.com
Avadhesh
Kumar
0000-0003-2206-5377
Department of Mathematics and Computer Science,
Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam(A.P.) - 515134, India
soni.iitkgp@gmail.com
10.22124/jmm.2020.16449.1447
This manuscript is concerned about the study of the existence and uniqueness of solutions for fractional differential equation involving Caputo Hadamard fractional operator of order $1 < vartheta leq 2$ with impulsive boundary conditions. The existence results are established firstly through the Banach Contraction Principle and then using Schauder's fixed point theorem. We present some examples to demonstrate the application of our main results.
Boundary value problem,impulses,Caputo-Hadamard fractional derivative,Fixed point theorem
https://jmm.guilan.ac.ir/article_4236.html
https://jmm.guilan.ac.ir/article_4236_d2a8b8fe278217652dd5a92bca133354.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Stability for coupled systems on networks with Caputo-Hadamard fractional derivative
107
118
EN
Hadjer
Belbali
Laboratoire de Mathematiques et Sciences appliquees, University of Ghardaia, Algeriaa
belbalihadjer3@gmail.com
Maamar
Benbachir
0000-0003-3519-1153
Faculty of Sciences, Saad Dahlab University, Blida, Algeria
mbenbachir2001@gmail.com
10.22124/jmm.2020.17303.1500
This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks<br />begin{equation*}<br /> left{<br /> begin{array}{l l l}<br /> ^{cH}D^{alpha} x_{i}=f_{i}(t,x_{i})+sumlimits_{j=1}^{n}g_{ij}(t,x_{i},x_{j}),&t> t_{0}, \ <br /> x_{i}(t_{0})=x_{i0},<br /> end{array}<br /> right.<br /> end{equation*}<br /> where $^{cH}D^{alpha} $ denotes the Caputo-Hadamard fractional derivative of order $ alpha $, $ 1<alphaleq 2 $, $ i=1,2,dots,n$, and $ f_{i}:mathbb{R}_{+}timesmathbb{R}^{m_i} to mathbb{R}^{m_i} $, $ g_{ij} : mathbb{R}_{+}times mathbb{R}^{m_i}times mathbb{R}^{m_j} to mathbb{R}^{m_i} $ are given functions. Based on graph theory and the classical Lyapunov technique, we prove stability and uniform asymptotic stability under suitable sufficient conditions. We also provide an example to illustrate the obtained results.
Fractional differential equation,Caputo-Hadamard,Coupled systems on networks,Lyapunov function
https://jmm.guilan.ac.ir/article_4239.html
https://jmm.guilan.ac.ir/article_4239_873afc1dd63e1fdb9b46a41d5d4f8369.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
On global existence and Ulam-Hyers stability of $Psi-$Hilfer fractional integrodifferential equations
119
135
EN
Vinod
Vijaykumar Kharat
Department~of~Mathematics, N. B. Navale Sinhgad College of Engg., Kegaon, Solapur-413255, India (M.S.)
vvkvinod9@gmail.com
Anand
Rajshekhar Reshimkar
Department of Mathematics, D. B. F. Dayanand College of Arts and Science, Solapur-413002, India (M.S.)
anand.reshimkar@gmail.com
10.22124/jmm.2020.16092.1405
In this sense, for this new fractional integrodifferential equation, we study the Ulam-Hyers and Ulam-Hyers-Rassias stability via successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and uniqueness via $epsilon-$approximated solution.
Ulam-Hyers stability,$Psi-$Hilfer fractional derivative,fractional integrodifferential equations,Banach fixed-point theorem
https://jmm.guilan.ac.ir/article_4256.html
https://jmm.guilan.ac.ir/article_4256_0e004567c0b16e881392e5d615eb5536.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
1
2021
01
01
Mathematical models for the variable weights version of the inverse minimax circle location problem
137
144
EN
Mehraneh
Gholami
Faculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran
mehraneh.gholami@gmail.com
Jafar
Fathali
Faculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran
fathali@shahroodut.ac.ir
10.22124/jmm.2020.16786.1455
This paper deals with the case of variable weights of the inverse model of the minimax circle location problem. The goal of the classic minimax circle location problem is finding a circle in the plane such that the maximum weighted distance from a given set of existing points to the circumference of the circle is minimized. In the corresponding inverse model, a circle is given and we should modify the weights of existing points with minimum cost, such that the given circle becomes optimal. The radius of the given circle can be fixed or variable. In this paper, both of these cases are investigated and mathematical models are presented for solving them.
Minimax circle location,inverse facility location,variable weights
https://jmm.guilan.ac.ir/article_4257.html
https://jmm.guilan.ac.ir/article_4257_beb557a38d1688d48e78ed4238d7ba18.pdf