The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

The quality of Global Navigation Satellite Systems (GNSS) networks are considerably influenced by the configuration of the observed baselines. Where, this study aims to find an optimal configuration for GNSS baselines in terms of the number and distribution  of baselines to improve the quality criteria of the GNSS networks. First order design problem (FOD) was applied in this research to optimize GNSS network baselines configuration, and based on sequential adjustment method to solve its objective functions.

FOD for optimum precision (FOD-p) was the proposed model which based on the design criteria of A-optimality and E-optimality. These design criteria were selected as objective functions of precision, whic

We examine the integrability in terms of Painlevè analysis for several models of higher order nonlinear solitary wave equations which were recently derived by Christou. Our results point out that these equations do not possess Painlevè property and fail the Painlevè test for some special values of the coefficients; and that indicates a non-integrability criteria of the equations by means of the Painlevè integrability.

Precision is one of the main elements that control the quality of a geodetic network, which defines as the measure of the network efficiency in propagation of random errors. This research aims to solve ZOD and FOD problems for a geodetic network using Rosenbrock Method to optimize the geodetic networks by using MATLAB programming language, to find the optimal design of geodetic network with high precision. ZOD problem was applied to a case study network consists of 19 points and 58 designed distances with a priori deviation equal to 5mm, to determine the best points in the network to consider as control points. The results showed that P55 and P73 having the minimum ellipse of error and considered as control points. FOD problem was applie

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.

     The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the converge

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

Let  be an n-Banach space, M be a nonempty closed convex subset of , and S:M→M be a mapping that belongs to the class  mapping. The purpose of this paper is to study the stability and data dependence results of a Mann iteration scheme on n-Banach space