University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
Equidistribution grids for two-parameter convectionâ€“diffusion boundary-value problems
1
21
EN
Jugal
Mohapatra
0000-0001-5118-3933
jugal@nitrkl.ac.in
In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uniform error bounds for the discrete solution are established. Numerical examples are carried out to show the performance of the proposed method on the adaptive grids.
Two,parameter singular perturbation problems,discontinuous coeffi,AMS Subject Classification : Keywords cient,boundary and interior layers,finite difference methods,adaptive grids
https://jmm.guilan.ac.ir/article_99.html
https://jmm.guilan.ac.ir/article_99_ca31ca0c8015b811d31bbe40790bfbac.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations
22
40
EN
Hossein
Aminikhah
hossein.aminikhah@gmail.com
Amir Hossein
Refahi Sheikhani
ah_refahi@yahoo.com
Hadi
Rezazadeh
rezazadehadi1363@gmail.com
The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results obtained by the proposed method show that the approach is very efficient, less computational and can be applied to other linear and nonlinear partial differential equations.
Laplace transform,partial differential equation,new homotopy pertur,bation method,fractional
https://jmm.guilan.ac.ir/article_100.html
https://jmm.guilan.ac.ir/article_100_cb34c32248c989022a1ac152a9f3d759.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
A numerical algorithm for solving a class of matrix equations
41
54
EN
Huamin
Zhang
zhangeasymail@126.com
Hongcai
Yin
hongcaiyin@sina.com
Rui
Ding
rding12@126.com
In this paper, we present a numerical algorithm for solving matrix equations $(A otimes B)X = F$Â by extending the well-known Gaussian elimination for $Ax = b$. The proposed algorithm has a high computational efficiency. Two numerical examples are provided to show the effectiveness of the proposed algorithm.
aussian elimination,Kronecker product,matrix equation
https://jmm.guilan.ac.ir/article_101.html
https://jmm.guilan.ac.ir/article_101_05bf065d7f2c614aff5cbc6474f5028e.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
Basic results on distributed order fractional hybrid differential equations with linear perturbations
55
73
EN
Hossein
Noroozi
hono1458@yahoo.com
Alireza
Ansari
alireza_1038@yahoo.com
In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschitz and Caratheodory conditions. Some basic fractional differential inequalities of distributed order are utilized to prove the existence of extremal solutions and comparison principle
Fractional hybrid differential equations,distributed order,extremal solutions,Banach algebra
https://jmm.guilan.ac.ir/article_102.html
https://jmm.guilan.ac.ir/article_102_b82e26b4e06c58afab2f6423d030cb3c.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
Arrival probability in the stochastic networks with an established discrete time Markov chain
74
89
EN
Gholam Hassan
Shirdel
shirdel81math@gmail.com
Mohsen
Abdolhosseinzadeh
a_m_stu@yahoo.com
The probable lack of some arcs and nodes in the stochastic networks is considered in this paper, and its effect is shown as the arrival probability from a given source node to a given sink node. A discrete time Markov chain with an absorbing state is established in a directed acyclic network. Then, the probability of transition from the initial state to the absorbing state is computed. It is assumed to have some wait states, if there is a physical connection but not any immediate communication between two nodes. The Numerical results show, the critical nodes and arcs are detected by the proposed method and it can be used to anticipate probable congestion in communication and transportation networks.
Stochastic networks,unstable networks,stochastic shortest path,discrete time Markov chain
https://jmm.guilan.ac.ir/article_103.html
https://jmm.guilan.ac.ir/article_103_ec9db26b80f3fa1d1ffa4b8dc1fc6dd9.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2
1
2014
05
01
Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations
90
106
EN
Mehdi
Bastani
bastani.mehdi@yahoo.com
In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.
Multistage variational iteration method,Convergence,HIV infection of CD4+ T cells,Adomian decomposition method
https://jmm.guilan.ac.ir/article_104.html
https://jmm.guilan.ac.ir/article_104_f77d0661b0b207e3d5c44d996f4086fd.pdf