مجله بین المللی محاسبات و مدل سازی ریاضی
سال هفتم شماره 1 (Winter 2017)

ýýýýýýýýýýýýýThis paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and productý. ýThe main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equationsý which appear in various fields of science such as physics and engineering. ýThe Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equationsý. ý
Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ýThe method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equationsý. ý
Illustrative examples are included to demonstrate the validity and efficiency of the presented methodý. It is further found that the absolute errors are almost constant in the studied interval. ýAlsoý, ýseveral theorems related to the convergence of the proposed methodý, ýwill be presentedýý.ý

The sinc method is known as an ecient 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.

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 con rm that the new schemes are non-oscillatory and yield sharp results when solving profi les 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.

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.

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.

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.