Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 7 1 (WINTER) 2017 01 01 Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations 1 25 EN Khadijeh Sadri Guilan University ssadri60@gmail.com Zainab Ayati Department of Engineerig Sciences&lrm;, &lrm;Faculty of Technology and Engineering East of Guilan ayati.zainab@gmail.com ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎<br /> which appear in various fields of science such as physics and engineering. ‎The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations‎. ‎<br /> Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ‎The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations‎. ‎Illustrative examples are included to demonstrate the validity and efficiency of the presented method‎. It is further found that the absolute errors are almost constant in the studied interval. ‎Also‎, ‎several theorems related to the convergence of the proposed method‎, ‎will be presented‎‎.‎ collocation method,Shifted Jacobi polynomials,System of Fredholm and Volterra integro-differential equations,Operational matrices of integration and product,‎Convergence http://ijm2c.iauctb.ac.ir/article_527368.html http://ijm2c.iauctb.ac.ir/article_527368_03795e7a5203dcd5810d836f4e06f79d.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 7 1 (WINTER) 2017 01 01 Multistage Modified Sinc Method for Solving Nonlinear Dynamical Systems 27 37 EN Hossein Kheiri University of Tabriz kheirihossein@yahoo.com Hossein Pourbashash . 123456789@name.com The sinc method is known as an ecient numerical method for solving ordinary or par-tial di erential equations but the system of di erential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical models in disease, the detailed stability analyses and numerical experiments are given on the standard within-host virus infections model. Sinc method,dynamical systems,the within-host virus model,Stability http://ijm2c.iauctb.ac.ir/article_528648.html http://ijm2c.iauctb.ac.ir/article_528648_6731991570be3717d95a0b56e75336b0.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 7 1 (WINTER) 2017 01 01 The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws 39 54 EN Rooholah Abedian University of Tehran, Faculty of Engineering, Department of Engineering Science rabedian@ut.ac.ir This work presents two high-order, semi-discrete, central-upwind schemes for<br /> computing approximate solutions of 1D systems of conservation laws. We propose a central<br /> weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order<br /> reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions<br /> with a semi-discrete central-upwind numerical <br /> flux and the third-order TVD Runge-Kutta<br /> method. Also this paper compares the numerical results of these two methods. Afterwards,<br /> we are interested in the behavior of the total variation (TV) of the approximate solution<br /> obtained with these schemes. We test these schemes on both scalar and gas dynamics<br /> problems. Numerical results con rm that the new schemes are non-oscillatory and yield sharp<br /> results when solving profi les with discontinuities. We also observe that the total variation<br /> of computed solutions is close to the total variation of the exact solution or a reference solution. CWENO technique,Central-Upwind schemes,Hyperbolic conservation laws,Total variation http://ijm2c.iauctb.ac.ir/article_531655.html http://ijm2c.iauctb.ac.ir/article_531655_ecab6486fe5b676897b5ce3baa7906d8.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 7 1 (WINTER) 2017 01 01 Influence of an external magnetic field on the peristaltic flow of a couple stress fluid through a porous medium. 55 65 EN Ajaz Dar Annamalai University darsalik88@gmail.com K Elangovan . 123456789@amin.com Magnetohydrodynamic(MHD) peristaltic flow of a Couple Stress Fluid through a permeable channel is examined in this investigation. The flow analysis is performed in the presence of an External Magnetic Field. Long wavelength and low Reynolds number approach is implemented.<br /> Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained.<br /> Pressure rise, frictional force and pumping phenomenon are portrayed and symbolized graphically.<br /> The elemental characteristics of this analysis is a complete interpretation of the influence of Couple Stress Parameter, magnetic number, non dimensional amplitude ratio and permeability parameter on the velocity, pressure gradient, pressure rise and frictional forces. Peristalsis,Couple Stress fluid,MHD flow,Reynold's number,pressure gradient http://ijm2c.iauctb.ac.ir/article_531656.html http://ijm2c.iauctb.ac.ir/article_531656_34db994e2bf505760c848c1771ef20bb.pdf