University of TabrizComputational Methods for Differential Equations2345-39826420181001A numerical approach for variable-order fractional unified chaotic systems with time-delay3964107678ENSholehYaghoobiDepartment of Mathematics, Lahijan Branch,
Islamic Azad University, Lahijan, IranBehrouzParsa MoghaddamDepartment of Mathematics, Lahijan Branch,
Islamic Azad University, Lahijan, Iran0000-0003-4957-9028KarimIvazTabriz universityJournal Article20170913This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To illustrate the effectiveness of the proposed scheme, dynamical behaviors of the variable-order fractional unified chaotic systems with time-delay are investigated in the time domain.https://cmde.tabrizu.ac.ir/article_7678_56a30376a636faf293a45a8899fd1e33.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001Solving singular integral equations by using orthogonal polynomials4114257703ENSamadAhdiaghdamDepartment of Mathematics, Marand Branch,
Islamic Azad University, Marand, IranJournal Article20171203In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solution of singular integral equations. The efficiency of the method is illustrated through some examples.https://cmde.tabrizu.ac.ir/article_7703_bfffa64cdafff69a1db80fda554e03a3.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001Space-time radial basis function collocation method for one-dimensional advection-diffusion problem4264377670ENMarziehKhaksarfardDepartment of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, IranYadollahOrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran0000-0002-5167-6874Mir SajjadHashemiDepartment of Mathematics, Basic Science Faculty,
Universiry of Bonab, Bonab, IranKobraKarimiDepartment of Mathematics, Buin Zahra Technical University,
Buin Zahra, Qazvin, IranJournal Article20170918The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validity of the presented method.https://cmde.tabrizu.ac.ir/article_7670_41fdd142453538f57cb04e13bb5ed69d.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system4384477715ENPegahMoghimiDepartment of Mathematical Sciences,
Isfahan University of Technology,
Isfahan, Iran, 84156-83111RasoulAsheghiDepartment of Mathematical Sciences,
Isfahan University of Technology,
Isfahan, Iran, 84156-83111RasoolKazemiDepartment of Mathematical Sciences,
University of Kashan, Kashan, Iran, 87317-53153Journal Article20171209In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =\langle I_0, I_1, I_2\rangle$, where $I_k(h)=\int_{H=h}x^ky\,dx$ and $H(x,y)=\frac{1}{2}y^2+\frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $h\in(0,\frac{1}{2})$. To this end, we use the criterion and tools developed by Grau et al. in \cite{Grau} to investigate when a collection of Abelian integrals is Chebyshev.https://cmde.tabrizu.ac.ir/article_7715_658154616797cb8e27927c86cb9b9d39.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001Chebyshev finite difference method for solving a mathematical model arising in wastewater treatment plants4484557669ENAbbasSaadatmandiDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan 87317-53153, Iran0000-0002-7744-7770SamanehFayyazDepartment of Chemical industries, Faculty of Valiasr, Tehran Branch,
Technical and Vocational University (TVU), Tehran, IranJournal Article20180131The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the problem to a set of algebraic equations. Numerical results are included to demonstrate the validity and applicability of the technique and a comparison is made with the existing results.https://cmde.tabrizu.ac.ir/article_7669_f61c52f9072cc754cbc511507c3f21cc.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001A total variation diminishing high resolution scheme for nonlinear conservation laws4564707677ENJavadFarziSahand university Of Technology,
P.O. Box 51335-1996, Tabriz, IranFayyazKhodadostiSahand university Of Technology,
P.O. Box 51335-1996, Tabriz, Iran0000-0003-4315-3907Journal Article20160731In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total variation diminishing (TVD). The TVD schemes are robust against the spurious oscillations and preserve the sharpness of the solution near the sharp discontinuities and shocks. We also, prove the positivity and maximum-principle properties for this scheme. The numerical results are presented for both of the advection and Burger’s equation. A comparison of numerical results with some classical limiter functions is also provided.https://cmde.tabrizu.ac.ir/article_7677_5d459469989103afafdfcf84fa49e253.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001A numerical technique for solving a class of 2D variational problems using Legendre spectral method4714827648ENKamalMamehrashiDepartment of Mathematics, Payame Noor University,
P. O. BOX 19395-3697, Tehran, Iran0000-0003-3663-2424FahimehSoltanianDepartment of Mathematics, Payame Noor University,
P. O. BOX 19395-3697, Tehran, Iran0000-0003-3068-3378Journal Article20180218An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage of the Ritz method is that it provides greater flexibility in which the boundary conditions are imposed at the end points of the interval. Furthermore, compared with the exact and eigenfunction solutions of the presented problems, the satisfactory results are obtained with low terms of basis elements. The convergence of the method is extensively discussed and finally two illustrative examples are included to demonstrate the validity and applicability of the proposed technique.https://cmde.tabrizu.ac.ir/article_7648_c2032555f7cdaa961e31d638d213cfd2.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001Rational Chebyshev Collocation approach in the solution of the axisymmetric stagnation flow on a circular cylinder4835007702ENAhmadGolbabaiSchool of Mathematics,
Iran University of Science and Technology, Tehran, IranSimaSamadpourSchool of Mathematics,
Iran University of Science and Technology, Tehran, IranJournal Article20171113In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper similarity transformations. The approach is named the rational Chebyshev collocation (RCC) method. This method reduces this nonlinear ordinary differential equation to an algebraic equations system. RCC method is a strong kind of the collocation technique to solve the problems of boundary value over a semi-infinite interval without truncating them to a finite domain. We also present the comparison of this work with others and show that the present method is more effective and precise.https://cmde.tabrizu.ac.ir/article_7702_893b99143ce525e40e03f36056999f13.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826420181001Homotopy perturbation method for eigenvalues of non-definite Sturm-Liouville problem5015077708ENFarhadDastmalchi SaeiDepartment of Mathematics, Tabriz Branch,
Islamic Azad University, Tabriz, IranJournal Article20161003In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.https://cmde.tabrizu.ac.ir/article_7708_88ba55bd7aa2e537894b27bdd1c7c54c.pdf