University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
Numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials
78
95
EN
M.
Behroozifar
Babol University of Technology
m_behroozifar@nit.ac.ir
S. A.
Yousefi
Shahid Beheshti University
s-yousefi@sbu.ac.ir
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.
Delay differential equation,Bernstein polynomial,Hybrid of block-pulse function,Operational matrix
http://cmde.tabrizu.ac.ir/article_307.html
http://cmde.tabrizu.ac.ir/article_307_17289efa2e1cc599ee284fe876cc5c65.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations
96
107
EN
Mohammadreza
Ahmadi Darani
Shahrekord University.
ahmadi.darani@sci.sku.ac.ir
Mitra
Nasiri
Shahrekord University.
mitra65nasiri@yahoo.com
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.
Chebyshev polynomials,orthogonal system,fractional differential equation,fractional-order Chebyshev functions,Operational matrix
http://cmde.tabrizu.ac.ir/article_598.html
http://cmde.tabrizu.ac.ir/article_598_0ef9db406547966aff664044ad1a9c85.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
A new numerical scheme for solving systems of integro-differential equations
108
119
EN
Esmail
Hesameddini
Shiraz University of Technology
Azam
Rahimi
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.
System of integro-differential equations,Volterra equation,Reconstruction of variational iteration method,Homotopy Perturbation method
http://cmde.tabrizu.ac.ir/article_588.html
http://cmde.tabrizu.ac.ir/article_588_4ab5f973114dd8420b112a7ca9ccee03.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations
120
134
EN
Hossein
Noroozi
Shahrekord University
hono1458@yahoo.com
Alireza
Ansari
Shahrekord University
alireza_1038@yahoo.com
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.
Fractional hybrid differential equations,Distributed order,Extremal solutions,Banach algebra
http://cmde.tabrizu.ac.ir/article_597.html
http://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
Lie symmetry analysis for Kawahara-KdV equations
135
145
EN
Ali
Haji Badali
University of Bonab
haji.badali@bonabu.ac.ir
Mir Sajjad
Hashemi
University of Bonab
hashemi@bonabu.ac.ir
Maryam
Ghahremani
University of Bonab
m_ghahremani90@yahoo.com
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.
Lie symmetries,Symmetry analysis,Optimal system,Infinitesimal Generators,Kawahara-KdV equation
http://cmde.tabrizu.ac.ir/article_971.html
http://cmde.tabrizu.ac.ir/article_971_26e06445c2a60e5b2c79259ca7107f29.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
1
2
2013
10
01
Solitary Wave solutions of the BK equation and ALWW system by using the first integral method
146
157
EN
Ahmad
Neirameh
Department of mathematics,Gonbad University
neirameh.edu@gmail.com
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.
First integral method,Broer-Kaup equations,Approximate long water wave equations
http://cmde.tabrizu.ac.ir/article_972.html
http://cmde.tabrizu.ac.ir/article_972_0e66618e8fc1bfb24782bd08578d30de.pdf