University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
Center manifold analysis and Hopf bifurcation of within-host virus model
266
279
EN
Hossein
Mohebbi
0000-0002-0591-9054
Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi
University of Technology, P. O. Box: 16315-1618, Tehran, Iran
ho.mohebbi@gmail.com
Azim
Aminataei
0000-0001-5247-4492
Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi
University of Technology, P. O. Box: 16315-1618, Tehran, Iran
ataei@kntu.ac.ir
Hossein
Pourbashash
Department of Mathematics, University of Garmsar,
P. O. Box: 3581755796, Garmsar, Iran
h.pourbashash@ugsr.ir
Anjila
Ataei Pirkooh
Department of Virology, School of Medicine,
Iran University of Medical Sciences, Tehran, Iran
ataei.a@iums.ac.ir
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<br /> and a locally asymptotically positive infection equilibrium appears.
Within-host virus model,Local and global stability,Center manifold,Reproduction number,Hopf Bifurcation
https://cmde.tabrizu.ac.ir/article_7433.html
https://cmde.tabrizu.ac.ir/article_7433_9f1264cddc71f632931face495f4c2bf.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations
280
294
EN
Avinash
Mittal
Discipline of Mathematics, IIITDM Jabalpur,
Madhya Pradesh 482005, India
avinash.mittal10@gmail.com
Lokendra
Balyan
Discipline of Mathematics, IIITDM Jabalpur,
Madhya Pradesh 482005, India
balyan@iiitdmj.ac.in
Dheeraj
Tiger
Department of Mathematics, Rajdhani College,
University of Delhi, India
dheerti@gmail.com
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
https://cmde.tabrizu.ac.ir/article_7450.html
https://cmde.tabrizu.ac.ir/article_7450_4d85f768649696abb38653f7e98f0fff.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
295
311
EN
Fahimeh
Akhavan Ghassabzade
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
Iran
akhavan_gh@yahoo.com
Jafar
Saberi_Nadjafi
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
Iran
najafi141@gmail.com
Ali Reza
Soheili
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
Iran
soheli@um.ac.ir
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
https://cmde.tabrizu.ac.ir/article_7449.html
https://cmde.tabrizu.ac.ir/article_7449_ed860972e6a9fe8c5ec1fed8287f79c1.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
Solving optimal control problems by PSO-SVM
312
325
EN
Elham
Salehpour
Department of Mathematics, Nowshahr branch,
Islamic Azad university, Nowshahr, Iran
salehpour.e61@gmail.com
Javad
Vahidi
Iran University of Science and Technology,
Information Technology Faculty, Tehran, Iran
jvahidi@iust.ac.ir
Hssan
Hossinzadeh
Department of Mathematics,
University of Mazandaran, Babolsar, Iran
hossinzadeh.h@umz.ac.ir
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
https://cmde.tabrizu.ac.ir/article_7413.html
https://cmde.tabrizu.ac.ir/article_7413_bd0a687beb2ed9d449fd232f8bfa1a41.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
Numerical studies of non-local hyperbolic partial differential equations using collocation methods
326
338
EN
khalid
Karam Ali
Mathematics Department, Faculty of Science, Al-Azhar University,
Nasr City (11884), Cairo, Egypt
khalidkaram2012@yahoo.com
Kamal
Raslan Raslan
Mathematics Department, Faculty of Science, Al-Azhar University,
Nasr City (11884), Cairo, Egypt
kamal_raslan@yahoo.com
Adel
Rashad Hadhoud
Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.
adelhadhoud_2005@yahoo.com
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
https://cmde.tabrizu.ac.ir/article_7412.html
https://cmde.tabrizu.ac.ir/article_7412_2ce6851006ad6b3a273cc9329787263f.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
An efficient extension of the Chebyshev cardinal functions for differential equations with coordinate derivatives of non-integer order
339
352
EN
Khosro
Sayevand
Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran
ksayehvand@yahoo.com
Hossein
Arab
Faculty of Mathematical Sciences, Malayer University,
P. O. Box 16846-13114, Malayer, Iran
h.a144@yahoo.com
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
https://cmde.tabrizu.ac.ir/article_7389.html
https://cmde.tabrizu.ac.ir/article_7389_1b7046be19abb6df10719883c800b696.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells
353
371
EN
Haman
Deilami Azodi
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
haman.d.azodi@gmail.com
Mohammad Reza
Yaghouti
0000-0003-3137-5799
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
yaghouti@guilan.ac.ir
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
https://cmde.tabrizu.ac.ir/article_7372.html
https://cmde.tabrizu.ac.ir/article_7372_f2b5599b36fc6b5f8bf2cc9d38ef1cfb.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
372
379
EN
Elham
Dastranj
Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran
dastranj.e@gmail.com
Seyed Reza
Hejazi
Department of mathematical sciences,
Shahrood university of technology,
Shahrood, Semnan, Iran
ra.hejazi@gmail.com
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
https://cmde.tabrizu.ac.ir/article_7371.html
https://cmde.tabrizu.ac.ir/article_7371_baaaa2b195339c4005c849a132e59816.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
3
2018
07
01
Numerical solution of Convection-Diffusion equations with memory term based on sinc method
380
395
EN
Atefeh
Fahim
Department of Mathematics, Faculty of Sciences, Central Tehran Branch, Islamic Azad University, Tehran, Iran
atefehfahim@yahoo.com
Mohammad Ali
Fariborzi Araghi
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
fariborzi.araghi@gmail.com
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
https://cmde.tabrizu.ac.ir/article_7390.html
https://cmde.tabrizu.ac.ir/article_7390_cb736ecdd13c490d00da7cbcecfc275e.pdf