In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the methods has been presented. In addition, the maximum error remainder () has been computed to demonstrate the accuracy of the proposed methods. The results persuasively prove that CM and D-CMs are reliable and accurate in obtaining the approximate solutions to the problems, with obvious superiority in accuracy for D-CMs than for CM.
Electromechanical actuators are used in a wide variety of aerospace applications such as missiles, aircrafts and spy-fly etc. In this work a linear and nonlinear fin actuator mathematical model has been developed and its response is investigated by developing an algorithm for the system using MATLAB. The algorithm used to the linear model is the state space algorithm while the algorithm used to the nonlinear model is the discrete algorithm. The huge moment constant is varied from (-3000 to 3000) and the damping ratio is varied from (0.4 to 0.8).
The comparison between linear and nonlinear fin actuator response results shows that for linear model, the maximum overshoot is about 10%,
... Show MoreSimple and sensitive kinetic methods are developed for the determination of Paracetamol in pure form and in pharmaceutical preparations. The methods are based on direct reaction (oxidative-coupling reaction) of Paracetamol with o-cresol in the presence of sodium periodate in alkaline medium, to form an intense blue-water-soluble dye that is stable at room temperature, and was followed spectrophotometriclly at λmax= 612 nm. The reaction was studied kinetically by Initial rate and fixed time (at 25 minutes) methods, and the optimization of conditions were fixed. The calibration graphs for drug determination were linear in the concentration ranges (1-7 μg.ml-1) for the initial rate and (1-10 μg.ml-1) for the fixed time methods at 25 min.
... Show MoreCerium oxide CeO2, or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the effect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,
... Show MoreCerium oxide (CeO2), or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the eect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,
... Show MoreThe 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.
In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.
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
... Show MoreIn this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions