2024-03-28T18:35:24Z
https://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=1000
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
Center manifold analysis and Hopf bifurcation of within-host virus model
Hossein
Mohebbi
Azim
Aminataei
Hossein
Pourbashash
Anjila
Ataei Pirkooh
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.
Within-host virus model
Local and global stability
Center manifold
Reproduction number
Hopf Bifurcation
2018
07
01
266
279
https://cmde.tabrizu.ac.ir/article_7433_9f1264cddc71f632931face495f4c2bf.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations
Avinash
Mittal
Lokendra
Balyan
Dheeraj
Tiger
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.
Generalized Burger-Huxley equation
Fitzhugh-Nagumo(FN) equation
Pseudospectral method
Chebyshev-Gauss-Lobbato points
2018
07
01
280
294
https://cmde.tabrizu.ac.ir/article_7450_4d85f768649696abb38653f7e98f0fff.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
Fahimeh
Akhavan Ghassabzade
Jafar
Saberi_Nadjafi
Ali Reza
Soheili
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.
Differential-difference equation
Boundary layer
Multiquadric collo- cation method
Radial basis function
2018
07
01
295
311
https://cmde.tabrizu.ac.ir/article_7449_ed860972e6a9fe8c5ec1fed8287f79c1.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
Solving optimal control problems by PSO-SVM
Elham
Salehpour
Javad
Vahidi
Hssan
Hossinzadeh
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.
particle swarm optimization
Support vector machines
Optimal control
2018
07
01
312
325
https://cmde.tabrizu.ac.ir/article_7413_bd0a687beb2ed9d449fd232f8bfa1a41.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
Numerical studies of non-local hyperbolic partial differential equations using collocation methods
khalid
Karam Ali
Kamal
Raslan Raslan
Adel
Rashad Hadhoud
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.
Collocation methods
Exponential cubic B-spline
Quintic B-spline
Finite difference
Wave equation
2018
07
01
326
338
https://cmde.tabrizu.ac.ir/article_7412_2ce6851006ad6b3a273cc9329787263f.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
An efficient extension of the Chebyshev cardinal functions for differential equations with coordinate derivatives of non-integer order
Khosro
Sayevand
Hossein
Arab
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.
Fractional differential equations
Chebyshev cardinal functions
Caputo fractional derivative
2018
07
01
339
352
https://cmde.tabrizu.ac.ir/article_7389_1b7046be19abb6df10719883c800b696.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells
Haman
Deilami Azodi
Mohammad Reza
Yaghouti
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.
Fourth kind Chebyshev wavelets
HIV model
Caputo derivative
2018
07
01
353
371
https://cmde.tabrizu.ac.ir/article_7372_f2b5599b36fc6b5f8bf2cc9d38ef1cfb.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
Elham
Dastranj
Seyed Reza
Hejazi
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.
Lie algebra
Geometric Brownian motion
Fokker Plank equation
Symmetry
2018
07
01
372
379
https://cmde.tabrizu.ac.ir/article_7371_baaaa2b195339c4005c849a132e59816.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2018
6
3
Numerical solution of Convection-Diffusion equations with memory term based on sinc method
Atefeh
Fahim
Mohammad Ali
Fariborzi Araghi
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.
Partial integro-differential equation
Sinc Collocation method
finite difference method
Product trapezoidal integration rule
Convection-diffusion equation
2018
07
01
380
395
https://cmde.tabrizu.ac.ir/article_7390_cb736ecdd13c490d00da7cbcecfc275e.pdf