University of TabrizComputational Methods for Differential Equations2345-39824220160401Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems991155432ENElmira AshpazzadehDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranMehrdad LakestaniDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranJournal Article20160804In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville integration and multiplication are then utilized to reduce the given optimization problem to the system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain algebraic equations. Illustrative examples are provided to confirm the applicability of the new method.University of TabrizComputational Methods for Differential Equations2345-39824220160401A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo1161275450ENSedighe ToubaeiIslamic Azad University, Ahvaz Branch, Ahvaz, IranMorteza GarshasbiDepartment of Mathematics, Iran University of Science and Technology, Tehran, IrannullMehdi JalalvandDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20160802In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reaction-diffusion equation. A computational approach based on finite difference and RBF-collocation methods is conducted to solve the equation with respect to the appropriate initial and boundary conditions. The ability and robustness of the numerical approach is investigated using two test problems.University of TabrizComputational Methods for Differential Equations2345-39824220160401Numerical solution of two-dimensional integral equations of the first kind by multi-step methods1281385510ENSeyed Musa TorabiDepartment of Mathematics, Shahed University, Tehran, IranAbolfazl Tari MarzabadDepartment of Mathematics, Shahed University, Tehran, IranJournal Article20160829In this paper, we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind. Here, we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods. We also verify convergence and error analysis of the method. At the end, we give some illustrative examples to show the efficiency and accuracy of the presented method.University of TabrizComputational Methods for Differential Equations2345-39824220160401Numerical solution of linear control systems using interpolation scaling functions1391505509ENBehzad Nemati SarayYoung Researchers and Elite Clube, Marand Branch,
Islamic Azad University, Marand, IranMohammad ShahriariDepartment of Mathematics, Faculty of Science,
University of Maragheh, Maragheh, IranJournal Article20160829The current paper proposes a technique for the numerical solution of linear control systems.The method is based on Galerkin method, which uses the interpolating scaling functions. For a highly accurate connection between functions and their derivatives, an operational matrix for the derivatives is established to reduce the problem to a set of algebraic equations. Several test problems are given, and the numerical results are reported to show the accuracy and efficiency of this method. University of TabrizComputational Methods for Differential Equations2345-39824220160401Stability analysis of a fractional order prey-predator system with nonmonotonic functional response1511615511ENReza Khoshsiar GhazianiDepartment of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, IranJavad AlidoustiDepartment of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, IranJournal Article20160919In this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator-prey oscillations. Therefore, antipredator behaviour helps the prey population to resist predator aggression.University of TabrizComputational Methods for Differential Equations2345-39824220160401Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet1621695512ENMehdi RamezaniDepartment of mathematics, Tafresh University,
Tafresh 39518 79611, IranJournal Article20161128The main purpose of this paper is to propose a new numerical method for solving the optimal control problems based on state parameterization. Here, the boundary conditions and the performance index are first converted into an algebraic equation or in other words into an optimization problem. In this case, state variables will be approximated by a new hybrid technique based on new second kind Chebyshev Wavelet.