2017
7
1
25
0
Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear IntegroDifferential Equations
2
2
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 integrodifferential 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 integrodifferential 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 integrodifferential 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.
1

1
25


Khadijeh
Sadri
Guilan University
Guilan University
Iran
ssadri60@gmail.com


Zainab
Ayati
Department of Engineerig Sciences‎, ‎Faculty of Technology and Engineering East of Guilan
Department of Engineerig Sciences‎,
Iran
ayati.zainab@gmail.com
collocation method
Shifted Jacobi polynomials
System of Fredholm and Volterra integrodifferential equations
Operational matrices of integration and product
Convergence
Multistage Modified Sinc Method for Solving Nonlinear Dynamical Systems
2
2
The sinc method is known as an ecient numerical method for solving ordinary or partial 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 Rungekutta 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 withinhost virus infections model.
1

27
37


Hossein
Kheiri
University of Tabriz
University of Tabriz
Iran
kheirihossein@yahoo.com


Hossein
Pourbashash
.
.
Iran
123456789@name.com
Sinc method
dynamical systems
the withinhost virus model
Stability
The comparison of two highorder semidiscrete central schemes for solving hyperbolic conservation laws
2
2
This work presents two highorder, semidiscrete, centralupwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially nonoscillatory (CWENO) reconstruction, also we apply a fourthorder reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semidiscrete centralupwind numerical flux and the thirdorder TVD RungeKutta 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 nonoscillatory 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.
1

39
54


Rooholah
Abedian
University of Tehran, Faculty of Engineering, Department of Engineering Science
University of Tehran, Faculty of Engineering,
Iran
rabedian@ut.ac.ir
CWENO technique
CentralUpwind schemes
Hyperbolic conservation laws
Total variation
Influence of an external magnetic field on the peristaltic flow of a couple stress fluid through a porous medium.
2
2
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.
1

55
65


Ajaz
Dar
Annamalai University
Annamalai University
Iran
darsalik88@gmail.com


K
Elangovan
.
.
Iran
123456789@amin.com
Peristalsis
Couple Stress fluid
MHD flow
Reynold's number
pressure gradient
Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature based radial basis functions
2
2
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.
1

67
77


Majid
Erfanian
University of Zabol
University of Zabol
Iran
erfaniyan@uoz.ac.ir


Sajad
Kosari
University of Zabol
University of Zabol
Iran
sajadkosari@yahoo.com
Radial Basis Function
differential quadrature
PDE
collocation method
Approximate solution of system of nonlinear Volterra integrodifferential equations by using Bernstein collocation method
2
2
This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of mth order nonlinear Volterra integrodifferential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integrodifferential 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 integrodifferential equations; The Bernstein polyno mials and series; Collocation points. 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20.
1

79
89


Sara
Davaeifar
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Ira
Department of Mathematics, Central Tehran
Iran
sara.davaei@yahoo.com


Jalil
Rashidinia
IUST and IAUCTB
IUST and IAUCTB
Iran
rashidinia@iust.ac.ir
Systems of nonlinear Volterra integrodifferential equations
The Bernstein polynomials and series
Operational matrices
Numerical matrix method
Collocation points