2021-09-19T03:02:34Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=715
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
A moving kriging interpolation-based meshfree method for solving two-phase elasticity system
Ameneh
Taleei
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
2021
01
01
1
12
https://jmm.guilan.ac.ir/article_4186_40f9b084970d75853cfa5b94d6b8ee6a.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
A combined dictionary learning and TV model for image restoration with convergence analysis
Souad
Mohaoui
Abdelilah
Hakim
Said
Raghay
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
2021
01
01
13
30
https://jmm.guilan.ac.ir/article_4187_8d48376485cc61654259b0f2dd2b02e0.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Lower bound approximation of nonlinear basket option with jump-diffusion
Yasser
Taherinasab
Ali Reza
Soheili
Mohammad
Amini
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.
Basket option
nonlinear stochastic differential equations
Poisson process
Split Step Backward Euler method
2021
01
01
31
44
https://jmm.guilan.ac.ir/article_4226_1b4d910cad60b8833e6f28bc1332a38b.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Almost periodic positive solutions for a time-delayed SIR epidemic model with saturated treatment on time scales
Kapula Rajendra
Prasad
Mahammad
Khuddush
Kuparala Venkata
Vidyasagar
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
2021
01
01
45
60
https://jmm.guilan.ac.ir/article_4230_9b40bcb9a3cfdf4fe20b7bb07b5f0e64.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Solving the Basset equation via Chebyshev collocation and LDG methods
Mohammad
Izadi
Mehdi
Afshar
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
2021
01
01
61
79
https://jmm.guilan.ac.ir/article_4231_c43909580b688d457545bf3290f7da3e.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
An RBF approach for oil futures pricing under the jump-diffusion model
Mohammad
Karimnejad Esfahani
Abdolsadeh
Neisy
Stefano
De Marchi
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
2021
01
01
81
92
https://jmm.guilan.ac.ir/article_4234_4601c4bfd9ea42954940b31531be8371.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Caputo-Hadamard fractional differential equation with impulsive boundary conditions
Ankit
Nain
Ramesh
Vats
Avadhesh
Kumar
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
2021
01
01
93
106
https://jmm.guilan.ac.ir/article_4236_d2a8b8fe278217652dd5a92bca133354.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Stability for coupled systems on networks with Caputo-Hadamard fractional derivative
Hadjer
Belbali
Maamar
Benbachir
This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks\begin{equation*} \left\{ \begin{array}{l l l} ^{cH}D^{\alpha} x_{i}=f_{i}(t,x_{i})+\sum\limits_{j=1}^{n}g_{ij}(t,x_{i},x_{j}),&t> t_{0}, \\ x_{i}(t_{0})=x_{i0}, \end{array} \right. \end{equation*} where $^{cH}D^{\alpha} $ denotes the Caputo-Hadamard fractional derivative of order $ \alpha $, $ 1<\alpha\leq 2 $, $ i=1,2,\dots,n$, and $ f_{i}:\mathbb{R}_{+}\times\mathbb{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
2021
01
01
107
118
https://jmm.guilan.ac.ir/article_4239_873afc1dd63e1fdb9b46a41d5d4f8369.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
On global existence and Ulam-Hyers stability of $Psi-$Hilfer fractional integrodifferential equations
Vinod
Vijaykumar Kharat
Anand
Rajshekhar Reshimkar
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
2021
01
01
119
135
https://jmm.guilan.ac.ir/article_4256_0e004567c0b16e881392e5d615eb5536.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
1
Mathematical models for the variable weights version of the inverse minimax circle location problem
Mehraneh
Gholami
Jafar
Fathali
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
2021
01
01
137
144
https://jmm.guilan.ac.ir/article_4257_beb557a38d1688d48e78ed4238d7ba18.pdf