Computational Methods for Differential EquationsComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Mon, 23 Jul 2018 12:27:14 +0100FeedCreatorComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Feed provided by Computational Methods for Differential Equations. Click to visit.Center manifold analysis and Hopf bifurcation of within-host virus model
http://cmde.tabrizu.ac.ir/article_7433_946.html
A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there exists a unique infectious equilibrium which may or may not be stable. In the case of instability, there exists an asymptotically stable periodic solution. Secondly, an analysis of local center manifold shows that when R0 = 1, a transcritical bifurcation occurs where upon increasing R0 greater than one the DFE loses stability and a locally asymptotically positive infection equilibrium appears. Sat, 30 Jun 2018 19:30:00 +0100A numerical technique for solving a class of 2D variational problems using Legendre spectral method
http://cmde.tabrizu.ac.ir/article_7648_0.html
An 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.Sat, 14 Jul 2018 19:30:00 +0100An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations
http://cmde.tabrizu.ac.ir/article_7450_946.html
In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main problem is reduced to a system of algebraic equations. This system is solved by standard numerical method. Numerical results for various cases of Generalized Burger-Huxley equation and other example of Fitzhugh- Nagumo equation are presented to demonstrate the performance and effectiveness of the method. Finaly, a comparison of our method with existing other methods available in literature are also given.Sat, 30 Jun 2018 19:30:00 +0100Chebyshev finite difference method for solving a mathematical model arising in wastewater ...
http://cmde.tabrizu.ac.ir/article_7669_0.html
The 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.Mon, 16 Jul 2018 19:30:00 +0100A method based on the meshless approach for singularly perturbed differential-difference ...
http://cmde.tabrizu.ac.ir/article_7449_946.html
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In fact, a set of uniform centers is distributed in the computational domain, and then coordinate stretching based transform is used to move the centers, to the region with high gradients. In addition to the integrated multiquadric (MQ) collocation method is applied to solve the transformed equation. The effectiveness of our method is demonstrated on several examples with boundary layer in both cases, i.e., boundary layer on the left side as well as the right side.Sat, 30 Jun 2018 19:30:00 +0100Space-time radial basis function collocation method for one-dimensional advection-diffusion problem
http://cmde.tabrizu.ac.ir/article_7670_0.html
The 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.Mon, 16 Jul 2018 19:30:00 +0100Solving optimal control problems by PSO-SVM
http://cmde.tabrizu.ac.ir/article_7413_946.html
The optimal control of problem is about finding a control law for a given system such that a certain optimality criterion is achieved. Methods of solving the optimal control problems are divided into direct methods and mediated methods (through other equations). In this paper, the PSO- SVM indirect method is used to solve a class of optimal control problems. In this paper, we try to determine the appropriate algorithm to improve our answers to problems.Sat, 30 Jun 2018 19:30:00 +0100Numerical studies of non-local hyperbolic partial differential equations using collocation methods
http://cmde.tabrizu.ac.ir/article_7412_946.html
The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accuracy and stability of the methods are assessed by applying it to the test problem. The results are found to be in good agreement with known solutions and with existing collocation schemes in literature.Sat, 30 Jun 2018 19:30:00 +0100An efficient extension of the Chebyshev cardinal functions for differential equations with ...
http://cmde.tabrizu.ac.ir/article_7389_946.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.Sat, 30 Jun 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_946.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.Sat, 30 Jun 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_946.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.Sat, 30 Jun 2018 19:30:00 +0100Numerical solution of Convection-Diffusion equations with memory term based on sinc method
http://cmde.tabrizu.ac.ir/article_7390_946.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, 30 Jun 2018 19:30:00 +0100