This paper deals with the numerical solution of the discrete classical optimal control problem (DCOCP) governing by linear hyperbolic boundary value problem (LHBVP). The method which is used here consists of: the GFEIM " the Galerkin finite element method in space variable with the implicit finite difference method in time variable" to find the solution of the discrete state equation (DSE) and the solution of its corresponding discrete adjoint equation, where a discrete classical control (DCC) is given.  The gradient projection method with either the Armijo method (GPARM) or with the optimal method (GPOSM) is used to solve the minimization problem which is obtained from the necessary conditi

This study has been undertaken to postulate the mechanism of impact test at low velocities. Thin-walled tubes of 100Cr6 were deformed under axial compression. In the present work there are seven velocities (4.429,4.652,5.240,5.600,5.942,6.264, 6.569) m\sec were applied to show how they effect the load, change in length, also the kinetic energy. However, the comparison between the obtained results and the other studies (Alexandar[3] , Abramowicz[4], Ayad[5]) was made the present work and Ayad data show good agreement. Load, change in length, kinetic energy were determined to understand the impact test.

In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered. The approximate solution is obtained in the form of splitting and applying the finite difference method (FDM). Moreover, this problem is ill-posed, dealing with instability of force after adding noise to the additional condition. To stabilize the solution, the regularization matrix is considered. Consequently, it is proved by error estimates between the regularized solution and the exact solution. The numerical results show that the method is efficient and stable.

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural

An evaluation was achieved by designing a matlab program to solve Kepler’s equation of an elliptical orbit for methods (Newton-Raphson, Danby, Halley and Mikkola). This involves calculating the Eccentric anomaly (E) from mean anomaly (M=0°-360°) for each step and for different values of eccentricities (e=0.1, 0.3, 0.5, 0.7 and 0.9). The results of E were demonstrated that Newton’s- Raphson Danby’s, Halley’s can be used for e between (0-1). Mikkola’s method can be used for e between (0-0.6).The term  that added to Danby’s method to obtain the solution of Kepler’s equation is not influence too much on the value of E. The most appropriate initial Gauss value was also determined to

A numerical method is developed to obtain two-dimensional velocity and pressure distribution through a cylindrical pipe with cross jet flows. The method is based on solving partial differential equations for the conservation of mass and momentum by finite difference method to convert them into algebraic equations. This well-known problem is used to introduce the basic concepts of CFD including: the finite- difference mesh, the discrete nature of the numerical solution, and the dependence of the result on the mesh refinement. Staggered grid implementation of the numerical model is used. The set of algebraic equations is solved simultaneously by “SIMPLE” algorithm to obtain velocity and pressure distribution within a pipe. In order to

The continuous increase in population has led to the development of underground structures like tunnels to be of great importance due to several reasons. One of these reasons is that tunnels do not affect the living activities on the surface, nor they interfere with the existing traffic network. More importantly, they have a less environmental impact than conventional highways and railways. This paper focuses on using numerical analysis of circular tunnels in terms of their behavior during construction and the deformations that may occur due to overburden and seismic loads imposed on them. In this study, the input data are taken from an existing Cairo metro case study; results were found for the lateral and vertical displacements, the Peak

 In this paper, we study the convergence theorems of the Modified Ishikawa iterative sequence with mixed errors for the uniformly continuous mappings and solving nonlinear uniformly continuous mappings equation in arbitrary real Banach space.