University of GuilanJournal of Mathematical Modeling2345-394X2120140501Equidistribution grids for two-parameter convection–diffusion boundary-value problems12199ENJugalMohapatraJournal Article20150521In 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.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X2120140501Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations2240100ENHosseinAminikhahAmir HosseinRefahi SheikhaniHadiRezazadehJournal Article20150521The 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.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X2120140501A numerical algorithm for solving a class of matrix equations4154101ENHuaminZhangHongcaiYinRuiDingJournal Article20150521In 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.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X2120140501Basic results on distributed order fractional hybrid differential equations with linear perturbations5573102ENHosseinNorooziAlirezaAnsariJournal Article20150521In 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 principlehttps://jmm.guilan.ac.ir/article_102_b82e26b4e06c58afab2f6423d030cb3c.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X2120140501Arrival probability in the stochastic networks with an established discrete time Markov chain7489103ENGholam HassanShirdelMohsenAbdolhosseinzadehJournal Article20150521The 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.https://jmm.guilan.ac.ir/article_103_ec9db26b80f3fa1d1ffa4b8dc1fc6dd9.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X2120140501Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations90106104ENMehdiBastaniJournal Article20150521In 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