In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

Recent growth in transport and wireless communication technologies has aided the evolution of Intelligent Transportation Systems (ITS). The ITS is based on different types of transportation modes like road, rail, ocean and aviation. Vehicular ad hoc network (VANET) is a technology that considers moving vehicles as nodes in a network to create a wireless communication network. VANET has emerged as a resourceful approach to enhance the road safety. Road safety has become a critical issue in recent years. Emergency incidents such as accidents, heavy traffic and road damages are the main causes of the inefficiency of the traffic flow. These occurrences do not only create the congestion on the road but also increase the fuel consumption and p

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

The modification of hydrophobic rock surfaces to the water-wet state via nanofluid treatment has shown promise in enhancing their geological storage capabilities and the efficiency of carbon dioxide (CO2) and hydrogen (H2) containment. Despite this, the specific influence of silica (SiO2) nanoparticles on the interactions between H2, brine, and rock within basaltic formations remains underexplored. The present study focuses on the effect of SiO2 nanoparticles on the wettability of Saudi Arabian basalt (SAB) under downhole conditions (323 K and pressures ranging from 1 to 20 MPa) by using the tilted plate technique to measure the contact angles between H2/brine and the rock surfaces. The findings reveal that the SAB's hydrophobicity intensif

This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi