Computational Methods for Differential EquationsComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Wed, 23 May 2018 05:54:55 +0100FeedCreatorComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Feed provided by Computational Methods for Differential Equations. Click to visit.New variants of the global Krylov type methods for linear systems with multiple right-hand ...
http://cmde.tabrizu.ac.ir/article_7218_946.html
In 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.Sat, 31 Mar 2018 19:30:00 +0100Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
http://cmde.tabrizu.ac.ir/article_7371_0.html
‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.Sun, 13 May 2018 19:30:00 +0100Matrix Mittag-Leffler functions of fractional nabla calculus
http://cmde.tabrizu.ac.ir/article_7147_946.html
In 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.Sat, 31 Mar 2018 19:30:00 +0100A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV ...
http://cmde.tabrizu.ac.ir/article_7372_0.html
This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integration is constructed for these wavelets. This matrix transforms the problem to a nonlinear system of algebraic equations. Solving the new system, enables one to identify the unknown coeffcients of expansion. Numerical results are compared with other existing methods to illustrate the applicability of the method.Sun, 13 May 2018 19:30:00 +0100Numerical quasilinearization scheme for the integral equation form of the Blasius ...
http://cmde.tabrizu.ac.ir/article_7181_946.html
‎The ‎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.‎Sat, 31 Mar 2018 19:30:00 +0100An efficient extension of the Chebyshev cardinal functions for differential equations with ...
http://cmde.tabrizu.ac.ir/article_7389_0.html
In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.Fri, 18 May 2018 19:30:00 +0100Numerical solution of nonlinear SPDEs using a multi-scale method
http://cmde.tabrizu.ac.ir/article_7203_946.html
‎In 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.Sat, 31 Mar 2018 19:30:00 +0100Numerical solution of Convection-Diffusion equations with memory term based on sinc method
http://cmde.tabrizu.ac.ir/article_7390_0.html
‎In this paper‎, ‎we study the numerical solution of Convection-Diffusion equation with a memory term subject to initial boundary value conditions‎. ‎Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc collocation method is employed in space‎. ‎The accuracy and error analysis of the method are discussed‎. ‎Numerical examples and illustrations are presented to prove the validity of the suggested method‎.Sat, 19 May 2018 19:30:00 +0100L2-transforms for boundary value problems
http://cmde.tabrizu.ac.ir/article_7202_946.html
In 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.Sat, 31 Mar 2018 19:30:00 +0100Approximate solution of the fuzzy fractional Bagley-Torvik equation by the RBF collocation method
http://cmde.tabrizu.ac.ir/article_7148_946.html
In 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.Sat, 31 Mar 2018 19:30:00 +0100The smoothed particle hydrodynamics method for solving generalized variable coefficient ...
http://cmde.tabrizu.ac.ir/article_7219_946.html
A 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.Sat, 31 Mar 2018 19:30:00 +0100An improved collocation method based on deviation of the error for solving BBMB equation
http://cmde.tabrizu.ac.ir/article_7220_946.html
In 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.Sat, 31 Mar 2018 19:30:00 +0100Discretization of a fractional order ratio-dependent functional response predator-prey model, ...
http://cmde.tabrizu.ac.ir/article_7182_946.html
This 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.Sat, 31 Mar 2018 19:30:00 +0100