Engineering and Applied Science Letters (EASL)

The purpose of this paper is to introduce and evaluate novel iterative methods for approximating solutions to nonlinear equations, which leverage the power of the variational iteration technique. Specifically, we present a comprehensive analysis of the proposed methods and demonstrate their effectiveness through various examples. Moreover, we provide a comparative analysis with other existing methods and conclude that the newly developed methods offer a competitive alternative. Our results highlight the potential of this approach in generating a diverse set of iterative methods for solving nonlinear equations. Therefore, this study contributes to the ongoing efforts to improve the efficiency and accuracy of nonlinear equation solving techniques.

The purpose of this study is to present a generalized class of estimators using the three-stage Optional Randomized Response Technique (ORRT) in the presence of non-response and measurement errors on a sensitive study variable. The proposed estimator makes use of dual auxiliary information. The expression for the bias and mean square error of the proposed estimator are derived using Taylor series expansion. The proposed estimator’s applicability is proven using real data sets. A numerical study is used to compare the efficiency of the proposed estimator with adapted estimators of the finite population mean. The suggested estimator performs better than adapted ordinary, ratio, and exponential ratio-type estimators in the presence of both non-response and measurement errors. The efficiency of the proposed estimator of population mean declines as the inverse sampling rate, non-response rate, and sensitivity level of the survey question increase.

Second-order macroscopic vehicular traffic flow models are categorized under two broad headings based on the direction of their characteristics. Faster-than-vehicle waves are often called isotropic models vis-\'{a}-vis anisotropic models with slower-than-vehicle characteristic speed. The dispute on the supremacy among these families of models is the motivation for this paper. This paper compares and contrasts six distinctive second-order macroscopic models using a numerical simulation and analysis. Three models are characterized by faster-than-vehicle waves with their corresponding anisotropic counterparts. Simulation results on the formation of deceleration waves and the dissolution of acceleration fans are presented to graphically compare the wave profiles of the selected isotropic and anisotropic traffic models. Observably, these opposing models can all characterize these physical traffic phenomena to the same degree. Thus, faster characteristic speed conceptualization of second-order macroscopic equations does not tantamount to model failure but rather lies in the explanation of this property.

In this paper, the comparative study of Fadugba-Falodun Scheme (FFS) and the Improved Euler’s Method (IEM) is presented. IEM and FFS have been used successfully for the solution of second order ordinary differential equation. FFS is a numerical method recently proposed by means of an interpolating function involving a transcendental function of exponential type. In order to discuss the efficiency and accuracy of the two methods, an illustrative example has been presented in the context of the Exact Solution (ES) and the absolute relative errors computed at each mesh point of the integration interval under consideration. The numerical results show that there is no significant difference between the FFS and ES, unlike its counterpart IEM. Hence, FFS is a good numerical method for the solution of the second order initial value problem in ordinary differential equations. All calculations have been carried out via MATLAB (R2014a) in double precision.

This paper is devoted to a study of the numerical solution of the thermoelastic model describing the contact problem between the body and a rigid foundation that is thermally conducting. The linear thermoelastic constitutive law describes the behavior of the material. The contact is frictionless and described with Signorini’s condition and a thermal contact condition when the heat exchange coefficient depends on the contact pressure. We aim to present a detailed description of the numerical modeling of the problem. on this end, we use a penalty method to approximate the constraints. Finally, we provide numerical simulations to study a two-dimensional example and compare the penalty problem with the Lagrangian one.

Poultry farms in Ghana are experiencing a decline, and some are at risk of collapsing due to the high cost of poultry feed. The aim of this paper is to assist poultry farmers in increasing their profits by reducing the cost of poultry feed. The linear programming technique is implemented to utilize locally available feed ingredients to formulate layer feed mix for the various stages of poultry growth, which includes chick mash (starter), grower, and prelayer. Mathematical models are constructed based on the nutrient requirements of the layers, nutrient composition of the available ingredients, and any other restrictions on the available ingredients for the formulation. Seven decision variables and eleven constraints are identified. Compared to the existing practice, it is estimated that the LP model’s optimal solution can reduce feed formulation costs by approximately 30%, 19%, and 14% in chick mash, grower, and prelayer, respectively.

In this paper, we formulate a new seven-step algorithm using a modified new iterative method for the numerical solution of the nonlinear gas dynamics equation. Three test cases are considered to demonstrate the feasibility and efficiency of the proposed method. Furthermore, numerical solutions show a good agreement with analytical solutions and some available examples from the available literature.

The “angle trisection-halting problem” impossibility analogy is fundamentally based on the obscure perception that; the classical geometric notion of constructability in Euclidean plane geometry corresponds to the modern theory of computability. Specifically, the difficulty of empirical trisectability of any angle has been viewed as analogous to the impossibility of solving the halting problem. The primary goal of this paper is to establish the inherent incompatibility between the geometric trisectioning of angles and the halting problem. The exposed proof concern the genetic solutions methodic characterization of the inconsistencies between the angle trisection problem and the halting problem. We show that regarding their attempts at solutions, the genetic trisectability of an arbitrary angle leads to solving the halting problem in geometric cryptographic schemes. It is upon the characteristic inconsistencies that we establish a provable refute of the validity of considering the practical applications of geometric cryptography as a solid source for cryptographic principles.

In a recent review paper related to energy storage, the authors noted that, in a bid to enhance the performance of the anode of a lithium-ion battery (LIB), that a part of the mechanism involved the ability of silicon (Si) and graphene oxide to bind, and that this process was aided by the ”mutual attraction of heterosexual charges” [1], a term or mechanism that was said to be derived from another paper [2]. A LIB, or any battery for that matter, does not have a bisexual, heterosexual or any sexual charge. It seems that this odd term and jargon neologism, or tortured phrase, was introduced as a result of mistranslation of an established term or jargon, ”opposite charges”. As such, it constitutes an error in need of correction. The wider implications for energy storage research such as LIBs, as well as for bibliometrics, are discussed.

The evolution of 4G networks has led to the development of different applications based on its powerful network capacity. Although, in the future with the presence of 5G (the fifth generation of network), the network of network, it is predicted that an incredible number of new services, with different business actors will be involved, are going to stem, exploit and explore. This paper briefly introduces the fifth generation of mobile network, 5G, in terms of capabilities, use cases and key enabling technologies, provides key concepts of information security, including availability, integrity and confidentiality. It also highlights the important of security in 5G landscape.