@article { author = {Mohebbi, Hossein and Aminataei, Azim and Pourbashash, Hossein and Ataei Pirkooh, Anjila}, title = {Center manifold analysis and Hopf bifurcation of within-host virus model}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {266-279}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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. }, keywords = {Within-host virus model,Local and global stability,Center manifold,Reproduction number,Hopf Bifurcation}, url = {https://cmde.tabrizu.ac.ir/article_7433.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7433_9f1264cddc71f632931face495f4c2bf.pdf} } @article { author = {Mittal, Avinash and Balyan, Lokendra and Tiger, Dheeraj}, title = {An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {280-294}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {Generalized Burger-Huxley equation,Fitzhugh-Nagumo(FN) equation,Pseudospectral method,Chebyshev-Gauss-Lobbato points}, url = {https://cmde.tabrizu.ac.ir/article_7450.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7450_4d85f768649696abb38653f7e98f0fff.pdf} } @article { author = {Akhavan Ghassabzade, Fahimeh and Saberi_Nadjafi, Jafar and Soheili, Ali Reza}, title = {A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {295-311}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {Differential-difference equation,Boundary layer,Multiquadric collo- cation method,Radial basis function}, url = {https://cmde.tabrizu.ac.ir/article_7449.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7449_ed860972e6a9fe8c5ec1fed8287f79c1.pdf} } @article { author = {Salehpour, Elham and Vahidi, Javad and Hossinzadeh, Hssan}, title = {Solving optimal control problems by PSO-SVM}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {312-325}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {particle swarm optimization,Support vector machines,Optimal control}, url = {https://cmde.tabrizu.ac.ir/article_7413.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7413_bd0a687beb2ed9d449fd232f8bfa1a41.pdf} } @article { author = {Karam Ali, khalid and Raslan Raslan, Kamal and Rashad Hadhoud, Adel}, title = {Numerical studies of non-local hyperbolic partial differential equations using collocation methods}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {326-338}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {Collocation methods,Exponential cubic B-spline,Quintic B-spline,Finite difference,Wave equation}, url = {https://cmde.tabrizu.ac.ir/article_7412.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7412_2ce6851006ad6b3a273cc9329787263f.pdf} } @article { author = {Sayevand, Khosro and Arab, Hossein}, title = {An efficient extension of the Chebyshev cardinal functions for differential equations with coordinate derivatives of non-integer order}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {339-352}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {Fractional differential equations,Chebyshev cardinal functions,Caputo fractional derivative}, url = {https://cmde.tabrizu.ac.ir/article_7389.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7389_1b7046be19abb6df10719883c800b696.pdf} } @article { author = {Deilami Azodi, Haman and Yaghouti, Mohammad Reza}, title = {A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {353-371}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {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.}, keywords = {Fourth kind Chebyshev wavelets,HIV model,Caputo derivative}, url = {https://cmde.tabrizu.ac.ir/article_7372.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7372_f2b5599b36fc6b5f8bf2cc9d38ef1cfb.pdf} } @article { author = {Dastranj, Elham and Hejazi, Seyed Reza}, title = {Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {372-379}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {‎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.}, keywords = {‎Lie algebra‎,‎Geometric Brownian motion‎,Fokker Plank equation‎,‎Symmetry‎}, url = {https://cmde.tabrizu.ac.ir/article_7371.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7371_baaaa2b195339c4005c849a132e59816.pdf} } @article { author = {Fahim, Atefeh and Fariborzi Araghi, Mohammad Ali}, title = {Numerical solution of Convection-Diffusion equations with memory term based on sinc method}, journal = {Computational Methods for Differential Equations}, volume = {6}, number = {3}, pages = {380-395}, year = {2018}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {‎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.}, keywords = {Partial integro-differential equation,Sinc Collocation method,finite difference method,Product trapezoidal integration rule,Convection-diffusion equation}, url = {https://cmde.tabrizu.ac.ir/article_7390.html}, eprint = {https://cmde.tabrizu.ac.ir/article_7390_cb736ecdd13c490d00da7cbcecfc275e.pdf} }