Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel

A simplified parallel key was presented in this work for the Taxa of Stackys L. wildly grown in Iraq. Three records within this genus were newly recorded to our country in the present work and they are S. kermanshahansis Rech S. setifera C.A. Mey. subsp setifera, S. setifera ssp iranica (Reck.) The characteristics of these new records were also given with some representative specimens.

In this study used three methods such as Williamson-hall, size-strain Plot, and Halder-Wagner to analysis x-ray diffraction lines to determine the crystallite size and the lattice strain of the nickel oxide nanoparticles and then compare the results of these methods with two other methods. The results were calculated for each of these methods to the crystallite size are (0.42554) nm, (1.04462) nm, and (3.60880) nm, and lattice strain are (0.56603), (1.11978), and (0.64606) respectively were compared with the result of Scherrer method (0.29598) nm,(0.34245),and the Modified Scherrer (0.97497). The difference in calculated results Observed for each of these methods in this study.

Secure information transmission over the internet is becoming an important requirement in data communication. These days, authenticity, secrecy, and confidentiality are the most important concerns in securing data communication. For that reason, information hiding methods are used, such as Cryptography, Steganography and Watermarking methods, to secure data transmission, where cryptography method is used to encrypt the information in an unreadable form. At the same time, steganography covers the information within images, audio or video. Finally, watermarking is used to protect information from intruders. This paper proposed a new cryptography method by using thre

The researcher wanted to make an attempt to identify the foundations of social solidarity, to strengthen the bonds of brotherhood among society, and spread the causes of compassion in the hearts of its members.
       The researcher has taken a short course in the hearts of the beloved to hearts.

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.