The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

  The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] .  Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

    This work is concerned with studying the solvability for optimal classical continuous control quaternary vector problem that controls by quaternary linear hyperbolic boundary value problem. The existence of the unique quaternary state vector solution for the quaternary linear hyperbolic boundary value problem  is studied and demonstrated by employing the method of Galerkin, where the classical continuous control quaternary vector  is Known. Also, the existence theorem of an optimal classical continuous control quaternary vector related to the quaternary linear hyperbolic boundary value problem is demonstrated. The existence of a unique solution to the adjoint quaternary linear hyperbolic boundary value problem a

The purpose of the current research is to identify the most important problems that primary school students suffer from inside and outside the classroom from the point of view of their teachers. A sample of (100) male and female teachers was chosen from the Rusafa\ second Directorate for the academic year (2018-2019). The research tool was prepared after reviewing literature related to the issue of problems and difficulties facing students or students in the school stage and even at university. The researcher reached several results that were discussed in the fourth chapter, with a set of conclusions based on the results of the research, and come up with several recommendations and suggestions.

Background:

      Throughout this paper, a generic iteration algorithm for a finite family of total asymptotically quasi-nonexpansive maps in uniformly convex Banach space is suggested. As well as weak / strong convergence theorems of this algorithm to a common fixed point are established. Finally, illustrative numerical example by using Matlab is presented.

The control of an aerial flexible joint robot (FJR) manipulator system with underactuation is a difficult task due to unavoidable factors, including, coupling, underactuation, nonlinearities, unmodeled uncertainties, and unpredictable external disturbances. To mitigate those issues, a new robust fixed-time sliding mode control (FxTSMC) is proposed by using a fixed-time sliding mode observer (FxTSMO) for the trajectory tracking problem of the FJR attached to the drones system. First, the underactuated FJR is comprehensively modeled and converted to a canonical model by employing two state transformations for ease of the control design. Then, based on the availability of the measured states, a cascaded FxTSMO (CFxTSMO) is constructed to estim

This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.