Equidistribution grids for two-parameter convection–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 https://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 https://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 $(A \otimes B)X = F$  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 https://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 https://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 probable congestion in communication and transportation networks. Journal of Mathematical Modeling University of Guilan 2345-394X 2 v. 1 no. 2014 74 89 https://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 https://jmm.guilan.ac.ir/article_104_f77d0661b0b207e3d5c44d996f4086fd.pdf