Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
Elmira
Ashpazzadeh
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
author
Mehrdad
Lakestani
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
99
115
http://cmde.tabrizu.ac.ir/article_5432_1b3c457da684d464a56954bafabf776f.pdf
A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo
Sedighe
Toubaei
Islamic Azad University, Ahvaz Branch, Ahvaz, Iran
author
Morteza
Garshasbi
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
author
Mehdi
Jalalvand
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
116
127
http://cmde.tabrizu.ac.ir/article_5450_561b40a6e09534b30701751945d7d27a.pdf
Numerical solution of two-dimensional integral equations of the first kind by multi-step methods
Seyed Musa
Torabi
Department of Mathematics, Shahed University, Tehran, Iran
author
Abolfazl
Tari Marzabad
Department of Mathematics, Shahed University, Tehran, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
128
138
http://cmde.tabrizu.ac.ir/article_5510_3923cafbddb9a05ae9297185cffa3e06.pdf
Numerical solution of linear control systems using interpolation scaling functions
Behzad
Nemati Saray
Young Researchers and Elite Clube, Marand Branch,
Islamic Azad University, Marand, Iran
author
Mohammad
Shahriari
Department of Mathematics, Faculty of Science,
University of Maragheh, Maragheh, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
139
150
http://cmde.tabrizu.ac.ir/article_5509_2d0b981480bf9ec6945dc84cf9c570ea.pdf
Stability analysis of a fractional order prey-predator system with nonmonotonic functional response
Reza
Khoshsiar Ghaziani
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
author
Javad
Alidousti
Department of Applied Mathematics and Computer Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
151
161
http://cmde.tabrizu.ac.ir/article_5511_ea0d5c86e39629903a940fb184caa5ef.pdf
Numerical solution of optimal control problems by using a new second kind Chebyshev wavelet
Mehdi
Ramezani
Department of mathematics, Tafresh University,
Tafresh 39518 79611, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
2
no.
2016
162
169
http://cmde.tabrizu.ac.ir/article_5512_b64ef39fd53732326b1eff6f131ff22f.pdf