eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
99
115
5432
Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
Elmira Ashpazzadeh
e.ashpazzadeh@gmail.com
1
Mehrdad Lakestani
cmde@tabrizu.ac.ir
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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.
http://cmde.tabrizu.ac.ir/article_5432_1b3c457da684d464a56954bafabf776f.pdf
Caputo fractional derivative
Fractional order optimal control
Biorthogonal cubic Hermite spline multiwavelets
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
116
127
5450
A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo
Sedighe Toubaei
stoobaei@yahoo.com
1
Morteza Garshasbi
m_garshasbi@iust.ac.ir
2
Mehdi Jalalvand
m.jalalvand@scu.ac.ir
3
Islamic Azad University, Ahvaz Branch, Ahvaz, Iran
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
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.
http://cmde.tabrizu.ac.ir/article_5450_561b40a6e09534b30701751945d7d27a.pdf
Reaction-diffusion
ecological systems
RBF collocation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
128
138
5510
Numerical solution of two-dimensional integral equations of the first kind by multi-step methods
Seyed Musa Torabi
sm.torabi@shahed.ac.ir
1
Abolfazl Tari Marzabad
tari@shahed.ac.ir
2
Department of Mathematics, Shahed University, Tehran, Iran
Department of Mathematics, Shahed University, Tehran, Iran
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.
http://cmde.tabrizu.ac.ir/article_5510_3923cafbddb9a05ae9297185cffa3e06.pdf
Two-dimensional nonlinear Volterra integral equations
Integral equations of the first kind
Multi-step methods
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
139
150
5509
Numerical solution of linear control systems using interpolation scaling functions
Behzad Nemati Saray
nemati.behzad@gmail.com
1
Mohammad Shahriari
shahriari@maragheh.ac.ir
2
Young Researchers and Elite Clube, Marand Branch, Islamic Azad University, Marand, Iran
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran
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.
http://cmde.tabrizu.ac.ir/article_5509_2d0b981480bf9ec6945dc84cf9c570ea.pdf
Linear control systems
Galerkin method
Interpolating scaling functions
Operational matrix
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
151
161
5511
Stability analysis of a fractional order prey-predator system with nonmonotonic functional response
Reza Khoshsiar Ghaziani
rkhoshsiar@gmail.com
1
Javad Alidousti
j.alidoosti@gmail.com
2
Department of Applied Mathematics and Computer Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics and Computer Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
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.
http://cmde.tabrizu.ac.ir/article_5511_ea0d5c86e39629903a940fb184caa5ef.pdf
Bifurcation
Fractional Prey-predator model
Stability of equilibrium
Dynamical behavior
Limit cycle
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-04-01
4
2
162
169
5512
Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet
Mehdi Ramezani
ramezani@tafreshu.ac.ir
1
Department of mathematics, Tafresh University, Tafresh 39518 79611, Iran
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.
http://cmde.tabrizu.ac.ir/article_5512_b64ef39fd53732326b1eff6f131ff22f.pdf
Second Kind Chebyshev Wavelet
Optimal Control Problems
Numerical analysis