University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
99
115
EN
Elmira
Ashpazzadeh
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
e.ashpazzadeh@gmail.com
Mehrdad
Lakestani
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
cmde@tabrizu.ac.ir
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 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.
Caputo fractional derivative,Fractional order optimal control,Biorthogonal cubic Hermite spline multiwavelets
http://cmde.tabrizu.ac.ir/article_5432.html
http://cmde.tabrizu.ac.ir/article_5432_1b3c457da684d464a56954bafabf776f.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo
116
127
EN
Sedighe
Toubaei
Islamic Azad University, Ahvaz Branch, Ahvaz, Iran
stoobaei@yahoo.com
Morteza
Garshasbi
null
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
m_garshasbi@iust.ac.ir
Mehdi
Jalalvand
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
m.jalalvand@scu.ac.ir
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 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.
Reaction-diffusion,ecological systems,RBF collocation
http://cmde.tabrizu.ac.ir/article_5450.html
http://cmde.tabrizu.ac.ir/article_5450_561b40a6e09534b30701751945d7d27a.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
Numerical solution of two-dimensional integral equations of the first kind by multi-step methods
128
138
EN
Seyed Musa
Torabi
Department of Mathematics, Shahed University, Tehran, Iran
sm.torabi@shahed.ac.ir
Abolfazl
Tari Marzabad
Department of Mathematics, Shahed University, Tehran, Iran
tari@shahed.ac.ir
In 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.
Two-dimensional nonlinear Volterra integral equations,Integral equations of the first kind,Multi-step methods
http://cmde.tabrizu.ac.ir/article_5510.html
http://cmde.tabrizu.ac.ir/article_5510_3923cafbddb9a05ae9297185cffa3e06.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
Numerical solution of linear control systems using interpolation scaling functions
139
150
EN
Behzad
Nemati Saray
Young Researchers and Elite Clube, Marand Branch,
Islamic Azad University, Marand, Iran
nemati.behzad@gmail.com
Mohammad
Shahriari
Department of Mathematics, Faculty of Science,
University of Maragheh, Maragheh, Iran
shahriari@maragheh.ac.ir
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.
Linear control systems,Galerkin method,Interpolating scaling functions,Operational matrix
http://cmde.tabrizu.ac.ir/article_5509.html
http://cmde.tabrizu.ac.ir/article_5509_2d0b981480bf9ec6945dc84cf9c570ea.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
Stability analysis of a fractional order prey-predator system with nonmonotonic functional response
151
161
EN
Reza
Khoshsiar Ghaziani
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
rkhoshsiar@gmail.com
Javad
Alidousti
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
j.alidoosti@gmail.com
In 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.
Bifurcation,Fractional Prey-predator model,Stability of equilibrium,Dynamical behavior,Limit cycle
http://cmde.tabrizu.ac.ir/article_5511.html
http://cmde.tabrizu.ac.ir/article_5511_ea0d5c86e39629903a940fb184caa5ef.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
2
2016
04
01
Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet
162
169
EN
Mehdi
Ramezani
Department of mathematics, Tafresh University,
Tafresh 39518 79611, Iran
ramezani@tafreshu.ac.ir
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.
Second Kind Chebyshev Wavelet,Optimal Control Problems,Numerical analysis
http://cmde.tabrizu.ac.ir/article_5512.html
http://cmde.tabrizu.ac.ir/article_5512_b64ef39fd53732326b1eff6f131ff22f.pdf