Equidistribution grids for two-parameter convectionâ€“diffusion boundary-value problems
Jugal
Mohapatra
author
text
article
2014
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
1
21
http://jmm.guilan.ac.ir/article_99_ca31ca0c8015b811d31bbe40790bfbac.pdf
Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations
Hossein
Aminikhah
author
Amir Hossein
Refahi Sheikhani
author
Hadi
Rezazadeh
author
text
article
2014
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
22
40
http://jmm.guilan.ac.ir/article_100_cb34c32248c989022a1ac152a9f3d759.pdf
A numerical algorithm for solving a class of matrix equations
Huamin
Zhang
author
Hongcai
Yin
author
Rui
Ding
author
text
article
2014
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
41
54
http://jmm.guilan.ac.ir/article_101_05bf065d7f2c614aff5cbc6474f5028e.pdf
Basic results on distributed order fractional hybrid differential equations with linear perturbations
Hossein
Noroozi
author
Alireza
Ansari
author
text
article
2014
eng
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
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
55
73
http://jmm.guilan.ac.ir/article_102_b82e26b4e06c58afab2f6423d030cb3c.pdf
Arrival probability in the stochastic networks with an established discrete time Markov chain
Gholam Hassan
Shirdel
author
Mohsen
Abdolhosseinzadeh
author
text
article
2014
eng
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 probablecongestion in communication and transportation networks.
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
74
89
http://jmm.guilan.ac.ir/article_103_ec9db26b80f3fa1d1ffa4b8dc1fc6dd9.pdf
Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations
Mehdi
Bastani
author
text
article
2014
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
2
v.
1
no.
2014
90
106
http://jmm.guilan.ac.ir/article_104_f77d0661b0b207e3d5c44d996f4086fd.pdf