eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
78
95
307
Numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials
M. Behroozifar
m_behroozifar@nit.ac.ir
1
S. A. Yousefi
s-yousefi@sbu.ac.ir
2
Babol University of Technology
Shahid Beheshti University
In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon expanding various time-varying functions as their truncated hybrid functions. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the method.
http://cmde.tabrizu.ac.ir/article_307_17289efa2e1cc599ee284fe876cc5c65.pdf
Delay differential equation
Bernstein polynomial
Hybrid of block-pulse function
Operational matrix
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
96
107
598
A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations
Mohammadreza Ahmadi Darani
ahmadi.darani@sci.sku.ac.ir
1
Mitra Nasiri
mitra65nasiri@yahoo.com
2
Shahrekord University.
Shahrekord University.
In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.
http://cmde.tabrizu.ac.ir/article_598_0ef9db406547966aff664044ad1a9c85.pdf
Chebyshev polynomials
orthogonal system
fractional differential equation
fractional-order Chebyshev functions
Operational matrix
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
108
119
588
A new numerical scheme for solving systems of integro-differential equations
Esmail Hesameddini
1
Azam Rahimi
2
Shiraz University of Technology
Shiraz University of Technology
This paper has been devoted to apply the Reconstruction of Variational Iteration Method (RVIM) to handle the systems of integro-differential equations. RVIM has been induced with Laplace transform from the variational iteration method (VIM) which was developed from the Inokuti method. Actually, RVIM overcome to shortcoming of VIM method to determine the Lagrange multiplier. So that, RVIM method provides rapidly convergent successive approximations to the exact solution. The advantage of the RVIM in comparison with other methods is the simplicity of the computation without any restrictive assumptions. Numerical examples are presented to illustrate the procedure. Comparison with the homotopy perturbation method has also been pointed out.
http://cmde.tabrizu.ac.ir/article_588_4ab5f973114dd8420b112a7ca9ccee03.pdf
System of integro-differential equations
Volterra equation
Reconstruction of variational iteration method
Homotopy Perturbation method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
120
134
597
Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations
Hossein Noroozi
hono1458@yahoo.com
1
Alireza Ansari
alireza_1038@yahoo.com
2
Shahrekord University
Shahrekord University
In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.
http://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdf
Fractional hybrid differential equations
Distributed order
Extremal solutions
Banach algebra
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
135
145
971
Lie symmetry analysis for Kawahara-KdV equations
Ali Haji Badali
haji.badali@bonabu.ac.ir
1
Mir Sajjad Hashemi
hashemi@bonabu.ac.ir
2
Maryam Ghahremani
m_ghahremani90@yahoo.com
3
University of Bonab
University of Bonab
University of Bonab
We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.
http://cmde.tabrizu.ac.ir/article_971_26e06445c2a60e5b2c79259ca7107f29.pdf
Lie symmetries
Symmetry analysis
Optimal system
Infinitesimal Generators
Kawahara-KdV equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-10-01
1
2
146
157
972
Solitary Wave solutions of the BK equation and ALWW system by using the first integral method
Ahmad Neirameh
neirameh.edu@gmail.com
1
Department of mathematics,Gonbad University
Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.
http://cmde.tabrizu.ac.ir/article_972_0e66618e8fc1bfb24782bd08578d30de.pdf
First integral method
Broer-Kaup equations
Approximate long water wave equations