2016
4
2
2
71
Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
2
2
In 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 RiemannLioville 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.
1

99
115


Elmira
Ashpazzadeh
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
Department of Applied Mathematics,
Faculty
I. R. Iran
e.ashpazzadeh@gmail.com


Mehrdad
Lakestani
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
Department of Applied Mathematics,
Faculty
I. R. Iran
cmde@tabrizu.ac.ir
Caputo fractional derivative
Fractional order optimal control
Biorthogonal cubic Hermite spline multiwavelets
A numerical treatment of a reactiondiffusion model of spatial pattern in the embryo
2
2
In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reactiondiffusion equation. A computational approach based on finite difference and RBFcollocation 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.
1

116
127


Sedighe
Toubaei
Islamic Azad University, Ahvaz Branch, Ahvaz, Iran
Islamic Azad University, Ahvaz Branch, Ahvaz,
I. R. Iran
stoobaei@yahoo.com


Morteza
Garshasbi
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
Department of Mathematics, Iran University
I. R. Iran
m_garshasbi@iust.ac.ir


Mehdi
Jalalvand
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Shahid Chamran
I. R. Iran
m.jalalvand@scu.ac.ir
Reactiondiffusion
ecological systems
RBF collocation
Numerical solution of twodimensional integral equations of the first kind by multistep methods
2
2
In this paper, we develop multistep methods to solve a class of twodimensional nonlinear Volterra integral equations (2DNVIEs) of the first kind. Here, we convert a 2DNVIE of the first kind to a onedimensional linear VIE of the first kind and then we solve the resulted equation numerically by multistep 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.
1

128
138


Seyed Musa
Torabi
Department of Mathematics, Shahed University, Tehran, Iran
Department of Mathematics, Shahed University,
I. R. Iran
sm.torabi@shahed.ac.ir


Abolfazl
Tari Marzabad
Department of Mathematics, Shahed University, Tehran, Iran
Department of Mathematics, Shahed University,
I. R. Iran
tari@shahed.ac.ir
Twodimensional nonlinear Volterra integral equations
Integral equations of the first kind
Multistep methods
Numerical solution of linear control systems using interpolation scaling functions
2
2
The 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.
1

139
150


Behzad
Nemati Saray
Young Researchers and Elite Clube, Marand Branch,
Islamic Azad University, Marand, Iran
Young Researchers and Elite Clube, Marand
I. R. Iran
nemati.behzad@gmail.com


Mohammad
Shahriari
Department of Mathematics, Faculty of Science,
University of Maragheh, Maragheh, Iran
Department of Mathematics, Faculty of Science,
Uni
I. R. Iran
shahriari@maragheh.ac.ir
Linear control systems
Galerkin method
Interpolating scaling functions
Operational matrix
Stability analysis of a fractional order preypredator system with nonmonotonic functional response
2
2
In this paper, we introduce fractional order of a planar fractional preypredator system with a nonmonotonic functional response and antipredator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that antipredator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predatorprey oscillations. Therefore, antipredator behaviour helps the prey population to resist predator aggression.
1

151
161


Reza
Khoshsiar Ghaziani
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics and Computer
I. R. Iran
rkhoshsiar@gmail.com


Javad
Alidousti
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics and Computer
I. R. Iran
j.alidoosti@gmail.com
Bifurcation
Fractional Preypredator model
Stability of equilibrium
Dynamical behavior
Limit cycle
Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet
2
2
The 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.
1

162
169


Mehdi
Ramezani
Department of mathematics, Tafresh University,
Tafresh 39518 79611, Iran
Department of mathematics, Tafresh University,
Taf
I. R. Iran
ramezani@tafreshu.ac.ir
Second Kind Chebyshev Wavelet
Optimal Control Problems
Numerical analysis