The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S

In this study, the adsorption of Zn (NO3)2 is carried out by using surfaces of malvaparviflora. The validity of the adsorption is evaluated by using atomic absorption Spectrophotometry through determination the amount of adsorbed Zn (NO3)2. Various parameters such as PH, adsorbent weight and contact time are studied in terms of their effect on the reaction progress. Furthermore, Lagergren’s equation is used to determine adsorption kinetics. It is observed that high removal of Zn (NO3)2 is obtained at PH=2. High removal of Zn (NO3)2 is at the time equivalent of 60 min and reaches equilibrium,where 0.25gm is the best weight of adsorbant . For kinetics the reaction onto malvaparviflora follows pseudo first order Lagergren’s equation.

This study aims to test ceramic waste's capacity to remove nickel from aqueous solutions through adsorption. Ceramic wastes were collected from the Refractories Manufacturing Plant in Ramadi. Through a series of lab tests, the reaction time (5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 minutes, and Ni concentrations (20, 40, 60, and 80) were tested using ceramic wastes with a solid to liquid ratio of 2g/30ml. At a temperature of 30ºC, the pH, total dissolved solids (TDS), and electrical conductivity (EC) were all measured. The equilibrium time was set at 30 min. Thereafter, the sorption (%) somewhat increased positively with the Ni concentration. Freundlich's equation showed that the adsorption intensity is 1.1827 and the Freundlich c

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

     The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.