Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations
Khadijeh
Sadri
Guilan University
author
Zainab
Ayati
Department of Engineerig Sciences‎, ‎Faculty of Technology and Engineering East of Guilan
author
text
article
2017
eng
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 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. 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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
1
25
http://ijm2c.iauctb.ac.ir/article_527368_5a3d799449afb386cd94fdceef9376c5.pdf
Multistage Modified Sinc Method for Solving Nonlinear Dynamical Systems
Hossein
Kheiri
University of Tabriz
author
Hossein
Pourbashash
.
author
text
article
2017
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
27
37
http://ijm2c.iauctb.ac.ir/article_528648_64e63d97ae248211670729e3275e0b6b.pdf
The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
Rooholah
Abedian
University of Tehran, Faculty of Engineering, Department of Engineering Science
author
text
article
2017
eng
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux and the third-order TVD Runge-Kutta method. Also this paper compares the numerical results of these two methods. Afterwards, we are interested in the behavior of the total variation (TV) of the approximate solution obtained with these schemes. We test these schemes on both scalar and gas dynamics problems. Numerical results conrm that the new schemes are non-oscillatory and yield sharp results when solving profiles with discontinuities. We also observe that the total variation of computed solutions is close to the total variation of the exact solution or a reference solution.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
39
54
http://ijm2c.iauctb.ac.ir/article_531655_225648e70e4b9f264dee7019c09fc730.pdf
Influence of an external magnetic field on the peristaltic flow of a couple stress fluid through a porous medium.
Ajaz
Dar
Annamalai University
author
K
Elangovan
.
author
text
article
2017
eng
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. Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained. Pressure rise, frictional force and pumping phenomenon are portrayed and symbolized graphically. 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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
55
65
http://ijm2c.iauctb.ac.ir/article_531656_dd8e5cee23a63bc7e5b89b8395e8ac55.pdf
Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Majid
Erfanian
University of Zabol
author
Sajad
Kosari
University of Zabol
author
text
article
2017
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
67
77
http://ijm2c.iauctb.ac.ir/article_534640_f2be3ba347bd951d02be1369a37a216e.pdf
Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
Sara
Davaeifar
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Ira
author
Jalil
Rashidinia
IUST and IAUCTB
author
text
article
2017
eng
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. Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno- mials and series; Collocation points. 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
7
v.
1
no.
2017
79
89
http://ijm2c.iauctb.ac.ir/article_535066_d76a8bb1569efc149061bca498f61646.pdf