eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
266
279
7433
Center manifold analysis and Hopf bifurcation of within-host virus model
Hossein Mohebbi
ho.mohebbi@gmail.com
1
Azim Aminataei
ataei@kntu.ac.ir
2
Hossein Pourbashash
h.pourbashash@ugsr.ir
3
Anjila Ataei Pirkooh
ataei.a@iums.ac.ir
4
Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16315-1618, Tehran, Iran
Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16315-1618, Tehran, Iran
Department of Mathematics, University of Garmsar, P. O. Box: 3581755796, Garmsar, Iran
Department of Virology, School of Medicine, Iran University of Medical Sciences, Tehran, Iran
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.
https://cmde.tabrizu.ac.ir/article_7433_9f1264cddc71f632931face495f4c2bf.pdf
Within-host virus model
Local and global stability
Center manifold
Reproduction number
Hopf Bifurcation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
280
294
7450
An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations
Avinash Mittal
avinash.mittal10@gmail.com
1
Lokendra Balyan
balyan@iiitdmj.ac.in
2
Dheeraj Tiger
dheerti@gmail.com
3
Discipline of Mathematics, IIITDM Jabalpur, Madhya Pradesh 482005, India
Discipline of Mathematics, IIITDM Jabalpur, Madhya Pradesh 482005, India
Department of Mathematics, Rajdhani College, University of Delhi, India
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.
https://cmde.tabrizu.ac.ir/article_7450_4d85f768649696abb38653f7e98f0fff.pdf
Generalized Burger-Huxley equation
Fitzhugh-Nagumo(FN) equation
Pseudospectral method
Chebyshev-Gauss-Lobbato points
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
295
311
7449
A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
Fahimeh Akhavan Ghassabzade
akhavan_gh@yahoo.com
1
Jafar Saberi_Nadjafi
najafi141@gmail.com
2
Ali Reza Soheili
soheli@um.ac.ir
3
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
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.
https://cmde.tabrizu.ac.ir/article_7449_ed860972e6a9fe8c5ec1fed8287f79c1.pdf
Differential-difference equation
Boundary layer
Multiquadric collo- cation method
Radial basis function
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
312
325
7413
Solving optimal control problems by PSO-SVM
Elham Salehpour
salehpour.e61@gmail.com
1
Javad Vahidi
jvahidi@iust.ac.ir
2
Hssan Hossinzadeh
hossinzadeh.h@umz.ac.ir
3
Department of Mathematics, Nowshahr branch, Islamic Azad university, Nowshahr, Iran
Iran University of Science and Technology, Information Technology Faculty, Tehran, Iran
Department of Mathematics, University of Mazandaran, Babolsar, Iran
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.
https://cmde.tabrizu.ac.ir/article_7413_bd0a687beb2ed9d449fd232f8bfa1a41.pdf
particle swarm optimization
Support vector machines
Optimal control
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
326
338
7412
Numerical studies of non-local hyperbolic partial differential equations using collocation methods
khalid Karam Ali
khalidkaram2012@yahoo.com
1
Kamal Raslan Raslan
kamal_raslan@yahoo.com
2
Adel Rashad Hadhoud
adelhadhoud_2005@yahoo.com
3
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.
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.
https://cmde.tabrizu.ac.ir/article_7412_2ce6851006ad6b3a273cc9329787263f.pdf
Collocation methods
Exponential cubic B-spline
Quintic B-spline
Finite difference
Wave equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
339
352
7389
An efficient extension of the Chebyshev cardinal functions for differential equations with coordinate derivatives of non-integer order
Khosro Sayevand
ksayehvand@yahoo.com
1
Hossein Arab
h.a144@yahoo.com
2
Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran
Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran
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.
https://cmde.tabrizu.ac.ir/article_7389_1b7046be19abb6df10719883c800b696.pdf
Fractional differential equations
Chebyshev cardinal functions
Caputo fractional derivative
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
353
371
7372
A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells
Haman Deilami Azodi
haman.d.azodi@gmail.com
1
Mohammad Reza Yaghouti
yaghouti@guilan.ac.ir
2
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
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.
https://cmde.tabrizu.ac.ir/article_7372_f2b5599b36fc6b5f8bf2cc9d38ef1cfb.pdf
Fourth kind Chebyshev wavelets
HIV model
Caputo derivative
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
372
379
7371
Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
Elham Dastranj
dastranj.e@gmail.com
1
Seyed Reza Hejazi
ra.hejazi@gmail.com
2
Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran
Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran
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.
https://cmde.tabrizu.ac.ir/article_7371_baaaa2b195339c4005c849a132e59816.pdf
Lie algebra
Geometric Brownian motion
Fokker Plank equation
Symmetry
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2018-07-01
6
3
380
395
7390
Numerical solution of Convection-Diffusion equations with memory term based on sinc method
Atefeh Fahim
atefehfahim@yahoo.com
1
Mohammad Ali Fariborzi Araghi
fariborzi.araghi@gmail.com
2
Department of Mathematics, Faculty of Sciences, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
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.
https://cmde.tabrizu.ac.ir/article_7390_cb736ecdd13c490d00da7cbcecfc275e.pdf
Partial integro-differential equation
Sinc Collocation method
finite difference method
Product trapezoidal integration rule
Convection-diffusion equation