A numerical solution of linear volterra integral equations of Second Kind with weakly singular kernel using the fifth order of non- polynomial spline functions

In this work , The fifth order non-polynomial spline functions is used to solve linear volterra integral equations with weakly singular kernel . Numerical examples are presented to illustrate the applications of this method and to compare the computed results with other numerical methods.

Numerical Simulation Stochastic of Differential Equations by Using Spline Function Approximations

In this paper, spline approximations with five collocation points are used for the numerical simulation of stochastic of differential equations(SDE). First, we have modeled continuous-valued discrete wiener process, and then numerical asymptotic stochastic stability of spline method is studied when applied to SDEs. The study shows that the method when applied to linear and nonlinear SDEs are stable and convergent. Moreover, the scheme is tested on two linear and nonlinear problems to illustrate the applicability and efficiency of the purposed method. Comparisons of our results with Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the our scheme is better than others.

Numerical Method for Finding Single and Multiple Integrals

In this paper, an iterative numerical method for obtaining approximate values of definite single, double and triple integrals will be illustrated. This method depends on approximating the single integral function by spline polynomial of fifth degree, while Gauss Legendre points as well as spline polynomials are used for finding multiple integrals. The study shows that when the method are applied to single integrals is convergent of order sixth, as well as when applied to triple integrals is convergent of order sixth for three Gauss Legendre points or greater. Errors estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method.

Design of Linear antenna array using Dolph-Chebyshev method

This paper illustrates a design of linear array antenna equal space and non uniform excitation using Dolph – Chebyshev method , We will discuss the designing procedure for antenna array having odd or even number of elements at two different values of the major to minor sidelobe level and at various between spaces , we will calculate the excitation coefficients and plot the radiation pattern for each case in addition to calculate both of the half power beam width angel and directivity. Finally : two curves will be plotted : first of them for beam broadening factor as a function of the major to minor sidelobe ratio ,the other one for directivity as a function of the array length.

Numerical Solution of Some Important Models of Partial Differential Equations Using Approximate - Analytical Methods ( ADM – VIM )

In this article, powerful approximate analytical methods, called Adomian decomposition method and variational iteration method are introduced and applied to obtaining the approximate analytical solutions for an important models of linear and non-linear partial differential equations such as ( nonlinear Klein Gordon equation - nonlinear wave equation - linear telegraph equation - nonlinear diffusion convection equation ) . The studied examples are used to reveal that those methods are very effective and convenient for solving linear and nonlinear partial differential equations . Numerical results and comparisons with the exact solution are included to show validity, ability, accuracy, strength and effectiveness of those techniques.

A Methodology for linking local coordinates system in Juba Darius with Public Coordinates System in Syria

Search includes the geodetic study local network triangulation real estate in Slenfeh area, and propose a solution for the local network linking public real estate network in Syria based on a comparison of the 2D-Transformation results so as to choose the optimal conversion which avoids the occurrence of interactions between regions and schemes real estate and reduces distortions network after conversion (shift, rotation, scale). At first been touched to date geodesic network set up in Slenfeh region and the stages of execution, and the problems of engineering, and then to the transformation methods used in the link, and apply them to the network, and choose the best conversion, and set parameters optimal transformation, have been proposed solution depends on the network is divided into three segments so that Network least deformation resulting from the transformation in each sector. A computer program that has been prepared for the implementation of the transformation and linking local grid points by using the C # programming language. It has been verified the resultant transformation parameters by comparing linear measurements calculated from coordinates resulting from the transformation with linear measurements in the network observation records, and execution field measurements of some of the points and calculate its coordinates and compare it with the coordinates calculating fromtransformation.

Spline Method with Three Collocation Parameters for Solving Ninth-Order General Differential Equations Subject to Boundary Conditions

In this paper, we use polynomial splines of eleventh degree with three collocation points to develop a method for computing approximations to the solution and its derivatives up to ninth order for general linear and nonlinear ninth-order boundary-value problems (BVPs). The study shows that the spline method with three collocation points when is applied to these problems is existent and unique. We prove that the proposed method if applied to ninth-order BVPs is stable and consistent of order eleven, and it possesses convergence rate greater than six. Finally, some numerical experiments are presented for illustrating the theoretical results and by comparing the results of our method with the other methods, we reveal that the proposed method is better than others.

Spline Method with Five Collocation Points for Solving Systems of High-Index Linear Differential Algebraic Equations

In this paper, we introduce a numerical method for solving systems of high-index differential algebraic equations. This method is based on approximating the exact solution by spline polynomial of degree eight with five collocation points to find the numerical solution in each step. The study shows that the method when applied to linear differential-algebraic systems with index equal one is stable and convergent of order 8, while it is stable and convergent of order 9-u for index equal u . Numerical experiments for four test examples and comparisons with other available results are given to illustrate the applicability and efficiency of the presented method

Calculating Characteristic Polynomial and Eigenspace of Plane Graph

This paper describes the Kasteleyn characteristic polynomial and the calcution of the eigenspaces of a plane graph. Therefore, this paper presents easy explicit formulas for if G is a simple plane graph.