University of TabrizComputational Methods for Differential Equations2345-39821220131001Numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials7895307ENM.BehroozifarBabol University of TechnologyS. A.YousefiShahid Beheshti UniversityJournal Article20131217<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.https://cmde.tabrizu.ac.ir/article_307_17289efa2e1cc599ee284fe876cc5c65.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39821220131001A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations96107598ENMohammadrezaAhmadi DaraniShahrekord University.MitraNasiriShahrekord University.Journal Article20140107In 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.https://cmde.tabrizu.ac.ir/article_598_0ef9db406547966aff664044ad1a9c85.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39821220131001A new numerical scheme for solving systems of integro-differential equations108119588ENEsmailHesameddiniShiraz University of TechnologyAzamRahimiShiraz University of TechnologyJournal Article20140121<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.https://cmde.tabrizu.ac.ir/article_588_4ab5f973114dd8420b112a7ca9ccee03.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39821220131001Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations120134597ENHosseinNorooziShahrekord UniversityAlirezaAnsariShahrekord UniversityJournal Article20140106In 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.https://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39821220131001Lie symmetry analysis for Kawahara-KdV equations135145971ENAliHaji BadaliUniversity of Bonab0000-0001-5309-5902Mir SajjadHashemiUniversity of BonabMaryamGhahremaniUniversity of BonabJournal Article20131225We 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.https://cmde.tabrizu.ac.ir/article_971_26e06445c2a60e5b2c79259ca7107f29.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39821220131001Solitary Wave solutions of the BK equation and ALWW system by using the first integral method146157972ENAhmadNeiramehDepartment of mathematics,Gonbad UniversityJournal Article20140120Solitary 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.https://cmde.tabrizu.ac.ir/article_972_0e66618e8fc1bfb24782bd08578d30de.pdf