eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 1 21 99 مقاله پژوهشی Equidistribution grids for two-parameter convection–diffusion boundary-value problems Jugal Mohapatra jugal@nitrkl.ac.in 1 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. https://jmm.guilan.ac.ir/article_99_ca31ca0c8015b811d31bbe40790bfbac.pdf Two parameter singular perturbation problems discontinuous coeffi AMS Subject Classification : Keywords cient boundary and interior layers finite difference methods adaptive grids eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 22 40 100 مقاله پژوهشی Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations Hossein Aminikhah hossein.aminikhah@gmail.com 1 Amir Hossein Refahi Sheikhani ah_refahi@yahoo.com 2 Hadi Rezazadeh rezazadehadi1363@gmail.com 3 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. https://jmm.guilan.ac.ir/article_100_cb34c32248c989022a1ac152a9f3d759.pdf Laplace transform partial differential equation new homotopy pertur bation method fractional eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 41 54 101 مقاله پژوهشی A numerical algorithm for solving a class of matrix equations Huamin Zhang zhangeasymail@126.com 1 Hongcai Yin hongcaiyin@sina.com 2 Rui Ding rding12@126.com 3 In this paper, we present a numerical algorithm for solving matrix equations \$(A otimes B)X = F\$  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. https://jmm.guilan.ac.ir/article_101_05bf065d7f2c614aff5cbc6474f5028e.pdf aussian elimination Kronecker product matrix equation eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 55 73 102 مقاله پژوهشی Basic results on distributed order fractional hybrid differential equations with linear perturbations Hossein Noroozi hono1458@yahoo.com 1 Alireza Ansari alireza_1038@yahoo.com 2 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 https://jmm.guilan.ac.ir/article_102_b82e26b4e06c58afab2f6423d030cb3c.pdf Fractional hybrid differential equations distributed order extremal solutions Banach algebra eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 74 89 103 مقاله پژوهشی Arrival probability in the stochastic networks with an established discrete time Markov chain Gholam Hassan Shirdel shirdel81math@gmail.com 1 Mohsen Abdolhosseinzadeh a_m_stu@yahoo.com 2 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. https://jmm.guilan.ac.ir/article_103_ec9db26b80f3fa1d1ffa4b8dc1fc6dd9.pdf Stochastic networks unstable networks stochastic shortest path discrete time Markov chain eng University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 2014-05-01 2 1 90 106 104 مقاله پژوهشی Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations Mehdi Bastani bastani.mehdi@yahoo.com 1 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. https://jmm.guilan.ac.ir/article_104_f77d0661b0b207e3d5c44d996f4086fd.pdf Multistage variational iteration method Convergence HIV infection of CD4+ T cells Adomian decomposition method