Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
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, ‎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_5a3d799449afb386cd94fdceef9376c5.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
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 ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential 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_64e63d97ae248211670729e3275e0b6b.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
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 conrm that the new schemes are non-oscillatory and yield sharp<br /> results when solving profiles 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_225648e70e4b9f264dee7019c09fc730.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
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_dd8e5cee23a63bc7e5b89b8395e8ac55.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
01
Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
67
77
EN
Majid
Erfanian
University of Zabol
erfaniyan@uoz.ac.ir
Sajad
Kosari
University of Zabol
sajadkosari@yahoo.com
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are applied to find the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Differential quadrature will introduce briefly and then we obtain the numerical solution of the PDEs. DQ is a numerical method for approximate and discretized partial derivatives of solution function. The key idea in DQ method is that any derivatives of unknown solution function at a mesh point can be approximated by weighted linear sum of all the functional values along a mesh line.
Radial Basis Function,differential quadrature,PDE,collocation method
http://ijm2c.iauctb.ac.ir/article_534640.html
http://ijm2c.iauctb.ac.ir/article_534640_f2be3ba347bd951d02be1369a37a216e.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
7
1
2017
11
01
Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
79
89
EN
Sara
Davaeifar
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Ira
sara.davaei@yahoo.com
Jalil
Rashidinia
IUST and IAUCTB
rashidinia@iust.ac.ir
This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising non linear system, the Bernstein coefficients can be determined to obtain the finite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach.<br /> Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno-<br /> mials and series; Collocation points.<br /> 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20.
Systems of nonlinear Volterra integro-differential equations,The Bernstein polynomials and series,Operational matrices,Numerical matrix method,Collocation points
http://ijm2c.iauctb.ac.ir/article_535066.html
http://ijm2c.iauctb.ac.ir/article_535066_d76a8bb1569efc149061bca498f61646.pdf