In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

  In this work, some of numerical methods for solving first order linear Volterra IntegroDifferential Equations are presented.      The numerical solution of these equations is obtained by using Open Newton Cotes formula.      The Open Newton Cotes formula is applied to find the optimum solution for this equation.      The computer program is written in (MATLAB) language (version 6)

        In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using  Mathcad 15.and graphic in Matlab R2015a.

In this paper, we present an approximate analytical and numerical solutions for the differential equations with multiple delay using the extend differential transform method (DTM). This method is used to solve many linear and non linear problems.

The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

       In this paper, we apply a new technique combined by a Sumudu transform and iterative method called the Sumudu iterative method for resolving non-linear partial differential equations to compute analytic solutions. The aim of this paper is to construct the efficacious frequent relation to resolve these problems. The suggested technique is tested on four problems. So the results of this study are debated to show how useful this method is in terms of being a powerful, accurate and fast tool with a little effort compared to other iterative methods.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].