University of TabrizComputational Methods for Differential Equations2345-39826220180401New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs1111277218ENGhodrat EbadiFaculty of Mathematical Sciences,
University of Tabriz, 51666-14766 Tabriz, IranSomaiyeh RashediFaculty of Mathematical Sciences,
University of Tabriz, 51666-14766 Tabriz, IranJournal Article20170420In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-BiCG and Gl-BiCR methods. The preconditioned versions of these methods are also explored in this study. Eventually, the efficiency of these approaches are demonstrated through numerical experimental results arising from two and three-dimensional advection dominated elliptic PDE.http://cmde.tabrizu.ac.ir/article_7218_d74a81e5c537c6a78b780d5dd92c2e64.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401Matrix Mittag-Leffler functions of fractional nabla calculus1281407147ENJagan Mohan JonnalagaddaDepartment of Mathematics, Birla Institute of Technology and Science Pilani,
Hyderabad-500078, Telangana, IndiaJournal Article20170204In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.http://cmde.tabrizu.ac.ir/article_7147_b05033af4cc006b63d709ae03a85e00d.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401Numerical quasilinearization scheme for the integral equation form of the Blasius equation1411567181ENEsmaeil NajafiDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, IranJournal Article20170605The method of quasilinearization is an effective tool to solve nonlinear equations when some conditions on the nonlinear term of the problem are satisfied. When the conditions hold, applying this technique gives two sequences of coupled linear equations and the solutions of these linear equations are quadratically convergent to the solution of the nonlinear problem. In this article, using some transformations, the well-known Blasius equation which is a nonlinear third order boundary value problem, is converted to a nonlinear Volterra integral equation satisfying the conditions of the quasilinearization scheme. By applying the quasilinearization, the solutions of the obtained linear integral equations are approximated by the collocation method. Employing the inverse of the transformation gives the approximation solution of the Blasius equation. Error analysis is performed and comparison of results with the other methods shows the priority of the proposed method.http://cmde.tabrizu.ac.ir/article_7181_2dc1887f3e3e26f8c1a03a3a1307787b.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401Numerical solution of nonlinear SPDEs using a multi-scale method1571757203ENMahmoud Mohammadi RoozbahaniFaculty of Mathematical Sciences, University of Guilan, P. O. Box 19141-41938, Rasht, IranHossein AminikhahFaculty of Mathematical Sciences, University of Guilan,
P. O. Box 19141–41938, Rasht, IranMahdieh TahmasebiFaculty of Mathematical Sciences, Tarbiat Modares University, P. O. Box 14115-134, Tehran, IranJournal Article20170501In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets. The method combines implicit collocation with the multi-scale method. Using the multi-scale method, SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain. The stability and consistency of the method are provided. Also numerical experiments illustrate the behavior of the proposed method.http://cmde.tabrizu.ac.ir/article_7203_fac381195a8ca2cb07a3e04222d53f24.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401L2-transforms for boundary value problems1761857202ENArman AghiliDepartment of applied mathematics, faculty of mathematical sciences,
University of Guilan, Rasht-Iran, P. O. Box 1841Journal Article20170606In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.http://cmde.tabrizu.ac.ir/article_7202_06bc3428c42a65aad44bf001229edbb0.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401Approximate solution of the fuzzy fractional Bagley-Torvik equation by the RBF collocation method1862147148ENMohsen EsmaeilbeigiDepartment of Mathematics, Faculty of Mathematics Science and Statistics,
Malayer University, Malayer 65719-95863, IranMahmoud ParipourDepartment of Computer Engineering and Information Technology,
Hamedan University of Technology, Hamedan 65155-579, IranGholamreza GarmanjaniDepartment of Mathematics, Faculty of Mathematics Science and Statistics,
Malayer University, Malayer 65719-95863, IranJournal Article20170209In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. The main advantage of this approach is that the fuzzy fractional Bagley-Torvik equation is reduced to the problem of solving two systems of linear equations. Determining a good shape parameter is still an outstanding research topic. To eliminate the effects of the radial basis function shape parameter, we use thin plate spline radial basis functions which have no shape parameter. The numerical investigation is presented in this paper shows that excellent accuracy can be obtained even when few nodes are used in analysis. Efficiency and effectiveness of the proposed procedure is examined by solving two benchmark problems.http://cmde.tabrizu.ac.ir/article_7148_a8e2799dc7b6c1ad8b3e71b41bd5eaa6.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401The smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system2152377219ENGholamreza KaramaliFaculty of Bsic Sciences, Shahid Sattari Aeronautical University of Sience and Technology,
South Mehrabad, Tehran, IranMostafa AbbaszadehFaculty of Bsic Sciences, Shahid Sattari Aeronautical University of Sience and Technology,
South Mehrabad, Tehran, IranMehdi DehghanDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology,
No. 424, Hafez Ave., 15914, Tehran, IranJournal Article20170728A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary differential equations (ODEs). Also, it is clear in the numerical methods for solving the time-dependent initial boundary value problems, based on the meshless methods, to achieve the high-order accuracy the temporal direction must be solved using an effective technique. Thus, in the current paper, we apply the fourth-order exponential time differenceing Runge-Kutta method (ETDRK4) for the obtained system of ODEs. The aim of this paper is to show that the meshless method based on the generalized SPH approach is suitable for the treatment of the nonlinear complex partial differential equations. Numerical examples confirm the efficiency of proposed scheme.http://cmde.tabrizu.ac.ir/article_7219_53260d81a325114d7affd1474cdc11ec.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401An improved collocation method based on deviation of the error for solving BBMB equation2382477220ENReza ParvazDepartment of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, IranMohammad ZarebniaDepartment of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, IranJournal Article20170704In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.http://cmde.tabrizu.ac.ir/article_7220_2fb10bac23a1e6594c9f8149de14d6f5.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826220180401Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos2482657182ENRazie Shafeii LashkarianDepartment of Basic science, Hashtgerd Branch,
Islamic Azad University, Alborz, IranDariush Behmardi SharifabadDepartment of Mathematics,
Alzahra university, Tehran, IranJournal Article20170130This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is not more of fractional order, exhibits much richer dynamical behavior than its corresponding fractional order model. Specially, in the discretized system, many types of bifurcations (transcritical, flip, Neimark-Sacker) and chaos may happen, however, the local analysis of the fractional-order counterpart, only deals with the stability (unstability) of the equilibria. Finally, some numerical simulations are performed by MATLAB, to support our analytic results.http://cmde.tabrizu.ac.ir/article_7182_b7136c735af5518730e4553adfc20658.pdf