Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Oscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.

  In this paper, we use the repeated corrected Simpson's 3/8 quadrature method for obtaining the numerical solutions of Fredholm linear integral equations of the second kind. This method is more accurately than the repeated corrected Trapezoidal method and the repeated Simpson's 3/8 method. To illustrate the accuracy of this method, we give a numerical example

In this work, an important sugar alkynyl ether has been synthesized in two subsequent steps starting from commercially available D-galactose (3). This kind of compounds is highly significant in the synthesis of biologically active molecules such as 1,2,3-triazole and isoxazoles. In the first step, galactose (3) was reacted with acetone in the presence of anhydrous copper (II) sulfate to produce 1,2:3,4-di-O-isopropylidene-α-D-galactose (4) in good yield. The latter was reacted with excess of 3-bromoprop-1-yne in DMF in the presence of NaOH pellets to afford the target molecule 5 in a very good yield. The temperature of this step is crucial in determining the reaction yi

Within this work, to promote the efficiency of organic-based solar cells, a series of novel A-π-D type small molecules were scrutinised. The acceptors which we designed had a moiety of N, N-dimethylaniline as the donor and catechol moiety as the acceptor linked through various conjugated π-linkers. We performed DFT (B3LYP) as well as TD-DFT (CAM-B3LYP) computations using 6-31G (d,p) for scrutinising the impact of various π-linkers upon optoelectronic characteristics, stability, and rate of charge transport. In comparison with the reference molecule, various π-linkers led to a smaller HOMO–LUMO energy gap. Compared to the reference molecule, there was a considerable red shift in the molecules under study (A1–A4). Therefore, based on

ספר תהילים הוא ספר מספרי המקרא, בתנ"ך היהודי הספר כלול בחלק הכתובים, ובביבליה הנוצרית מכונה הספר Ψαλμός בת

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.