In this paper, the linear system of Fredholm integral equations is solving using Open Newton-Cotes formula, which we use five different types of Open Newton-Cotes formula to solve this system.  Compare the results of suggested method with the results of another method (closed Newton-Cotes formula)    Finally, at the end of each method, algorithms and programs developed and written in MATLAB (version 7.0) and we give some numerical examples, illustrate suggested method

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

In this research we have been studied the 3rd order spherical aberration for an optical system consisted of obscured circular aperture with non central circular obscuration through the calculation of point spread function (P.S.F) in presence of the obscuration in the center and comparing the obtained results with that results of moving obscuration far away from the center, where the results showed significant improvement for(P.S.F) value. The study was done of different obscurities ratios in addition to the different 3rd order spherical aberration values (W40=0.25 ,0.5 ,0.75 ,1 ).

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.