University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 Numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials 78 95 307 EN M. Behroozifar Babol University of Technology S. A. Yousefi Shahid Beheshti University Journal Article 2013 12 17 <br />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 https://cmde.tabrizu.ac.ir/article_307_17289efa2e1cc599ee284fe876cc5c65.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations 96 107 598 EN Mohammadreza Ahmadi Darani Shahrekord University. Mitra Nasiri Shahrekord University. Journal Article 2014 01 07 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 https://cmde.tabrizu.ac.ir/article_598_0ef9db406547966aff664044ad1a9c85.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 A new numerical scheme for solving systems of integro-differential equations 108 119 588 EN Esmail Hesameddini Shiraz University of Technology Azam Rahimi Shiraz University of Technology Journal Article 2014 01 21 <br />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 https://cmde.tabrizu.ac.ir/article_588_4ab5f973114dd8420b112a7ca9ccee03.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations 120 134 597 EN Hossein Noroozi Shahrekord University Alireza Ansari Shahrekord University Journal Article 2014 01 06 In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation<br />$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$<br />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 https://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 Lie symmetry analysis for Kawahara-KdV equations 135 145 971 EN Ali Haji Badali University of Bonab Mir Sajjad Hashemi University of Bonab Maryam Ghahremani University of Bonab Journal Article 2013 12 25 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 https://cmde.tabrizu.ac.ir/article_971_26e06445c2a60e5b2c79259ca7107f29.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 1 2 2013 10 01 Solitary Wave solutions of the BK equation and ALWW system by using the first integral method 146 157 972 EN Ahmad Neirameh Department of mathematics,Gonbad University Journal Article 2014 01 20 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 https://cmde.tabrizu.ac.ir/article_972_0e66618e8fc1bfb24782bd08578d30de.pdf