University of TabrizComputational Methods for Differential Equations2345-39826320180701Center manifold analysis and Hopf bifurcation of within-host virus model2662797433ENHossein MohebbiDepartment of Applied Mathematics, Faculty of Mathematics, K. N. Toosi
University of Technology, P. O. Box: 16315-1618, Tehran, Iran0000-0002-0591-9054Azim AminataeiDepartment of Applied Mathematics, Faculty of Mathematics, K. N. Toosi
University of Technology, P. O. Box: 16315-1618, Tehran, IranHossein PourbashashDepartment of Mathematics, University of Garmsar,
P. O. Box: 3581755796, Garmsar, IranAnjila Ataei PirkoohDepartment of Virology, School of Medicine,
Iran University of Medical Sciences, Tehran, IranJournal Article20170729A 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. https://cmde.tabrizu.ac.ir/article_7433_9f1264cddc71f632931face495f4c2bf.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations2802947450ENAvinash MittalDiscipline of Mathematics, IIITDM Jabalpur,
Madhya Pradesh 482005, IndiaLokendra BalyanDiscipline of Mathematics, IIITDM Jabalpur,
Madhya Pradesh 482005, IndiaDheeraj TigerDepartment of Mathematics, Rajdhani College,
University of Delhi, IndiaJournal Article20170822In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers2953117449ENFahimeh Akhavan GhassabzadeDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
IranJafar Saberi_NadjafiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
IranAli Reza SoheiliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad,
IranJournal Article20170719In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701Solving optimal control problems by PSO-SVM3123257413ENElham SalehpourDepartment of Mathematics, Nowshahr branch,
Islamic Azad university, Nowshahr, IranJavad VahidiIran University of Science and Technology,
Information Technology Faculty, Tehran, IranHssan HossinzadehDepartment of Mathematics,
University of Mazandaran, Babolsar, IranJournal Article20170113The 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701Numerical studies of non-local hyperbolic partial differential equations using collocation methods3263387412ENkhalid Karam AliMathematics Department, Faculty of Science, Al-Azhar University,
Nasr City (11884), Cairo, EgyptKamal Raslan RaslanMathematics Department, Faculty of Science, Al-Azhar University,
Nasr City (11884), Cairo, EgyptAdel Rashad HadhoudMathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.Journal Article20180109The 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701An efficient extension of the Chebyshev cardinal functions for differential equations with coordinate derivatives of non-integer order3393527389ENKhosro SayevandFaculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, IranHossein ArabFaculty of Mathematical Sciences, Malayer University,
P. O. Box 16846-13114, Malayer, IranJournal Article20170714In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells3533717372ENHaman Deilami AzodiFaculty of Mathematical Sciences, University of Guilan, Rasht, IranMohammad Reza YaghoutiFaculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20170711This 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries3723797371ENElham DastranjDepartment of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, IranSeyed Reza HejaziDepartment of mathematical sciences,
Shahrood university of technology,
Shahrood, Semnan, IranJournal Article20170305In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39826320180701Numerical solution of Convection-Diffusion equations with memory term based on sinc method3803957390ENAtefeh FahimDepartment of Mathematics, Faculty of Sciences, Central Tehran Branch, Islamic Azad University, Tehran, IranMohammad Ali Fariborzi AraghiDepartment of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, IranJournal Article20170619In 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