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The purpose of this paper is to assess the perspectives of law enforcement executives and public school principals regarding school resource officers (SROs), armed teachers, and armed school administrators in order to inform the policy discussion surrounding school safety issues.

This study utilizes data collected from two surveys that were sent to law enforcement executives and public school principals in South Carolina. Respondents were asked about their experience with SROs and their perspectives on these officers’ ability to maintain school safety. Both groups of respondents were also asked about their attitudes regarding arming school employees.

There is a large amount of support for SROs from both law enforcement executives and principals. However, in general, both groups of respondents do not believe armed administrators or armed teachers to be an effective school safety strategy.

SROs have been the primary strategy adopted by schools to maintain safety, but in the wake of the shooting at Sandy Hook Elementary School, public outcry and political debate has spawned a number of proposed alternatives. Among these alternative security measures has been the idea of arming school teachers and/or administrators. However, there appears to have been little effort to empirically consider the perspectives of those directly impacted by school safety policy decisions. In particular, a gap in the literature remains regarding the perceptions of police executives and school principals concerning school safety policies and how the attitudes of these key actors compare. Thus, the current study addresses this gap by exploring the perspectives of key school safety stakeholders.

The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs).

A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter.

To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem.

The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

It is undeniable that the annular fin of hyperbolic profile with constant thermal conductivity and uniform convective coefficient is important in many applications of heat transfer engineering. The importance of this fin configuration stems from its close resemblance to the annular fin of optimal cross section capable of delivering maximum heat transfer for a given volume of material. This paper addresses two simple numerical procedures for solving the generalized Bessel equation that governs the temperature variation in annular fins of hyperbolic profile, one is the finite‐difference technique with an uncharacteristic coarse mesh and the other is the shooting method. Certainly, the central objective here is to avoid the evaluation of the elegant, but intricate exact analytic temperature distributions and companion fin efficiencies containing modified Bessel functions of fractional order.

The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring shooting technique and analytically via a new modified analytical technique called improved generalized Adomian decomposition method (improved-GDM).

It is well established that the generalized decomposition method (GDM) (Yong-Chang et al., 2008), which uses a new kind of decomposition strategy for the nonlinear function, has proved its efficiency and superiority when compared to the standard ADM method. In this investigation, based on the idea of improved-ADM method developed by Lina and Song (Song and Wang, 2013), the authors proposed a new analytical algorithm of computation named improved-GDM. Thereafter, the proposed algorithm is tested by solving the nonlinear problem of the hydro-magnetic boundary layer flow over a flat plate.

The proposed improved generalized decomposition method (I-GDM) introduces a convergence-control parameter “ω’’ into the GDM, which accelerates the convergence of solution and reduces considerably the computation time. In fact, the key of this method is mainly based on the best selection of the convergence-control parameter ω.

The paper presents a new efficient algorithm of computation that can be considered as an alternative for solving the nonlinear initial boundary layer value problems. Obtained results show clearly the accuracy of the proposed method.

The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

The purpose of this paper is to demonstrate an effective and robust numerical solution for Raman fiber amplifier (RFA) equations which have no explicit solution. MATLAB BVP solvers are addressed for the solution.

The continuation method proposed for the solution of RFA equations using MATLAB BVP solvers is explained. Scripts for improving the power values at the boundaries with continuation, extending fiber length with continuation and calculation of the analytical partial derivatives using the MATLAB Symbolic toolbox are introduced. Comparisons among the different MATLAB BVP solvers have been made. Using the continuation method, signal evolutions for different kinds of RFA amplifier configurations are plotted.

The paper finds that MATLAB BVP solver with the continuation method can be used in the design of various kinds of RFAs for high powers/long gain fiber spans.

The paper will assist the fiber optic research community who suffer from two or more point boundary‐value problems. Moreover, the stiffness of the signal evolution which is faced with high pump powers and/or long fiber lengths can be solved with continuation. This superiority of the solver can be used to overcome any stiff changes of the signals for future studies.

The increased research interests and practical demands for RFAs have been calling for reasonable and efficient means for the performance evaluation of RFAs before the real amplifiers are fabricated. The solution method presented in this paper will be an efficient means for the solution of this issue.

MATLAB BVP solvers have been proven to be effective for the numerical solution of RFAs with multiple pumps and signal waves. Using the continuation method, in a distributed RFA with ten pump sources, 2,400 mW total input pump power is achieved. The improvement of the total power is about 1.4 times compared with those of the previously reported methods. Using the MATLAB BVP solvers, total power/fiber span can be improved further using the continuation process with the cost of computational time. This is a notable and promising improvement from a RFA designer's point of view.

The purpose of this paper is to investigate the approximate solution of the couple stress fluid equations in a semi‐infinite rectangular channel with porous and uniformly expanding or contracting walls.

Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real‐life nonlinear problems. The governing partial differential equations are transformed using a transformation into an ordinary differential equation that is solved by homotopy analysis method (HAM) and shooting technique.

To assess the accuracy of the solutions, the comparison of the obtained results reveals that both methods are tremendously effective. Analytical and numerical solutions comparison indicates an excellent agreement and this comparison is also presented. Graphs are portrayed for the effects of some values of parameters.

Expansion or contraction problems occur naturally in the transport of biological fluids, the air circulation in the respiratory system, expanding or contracting jets and the synchronous pulsating of porous diaphragms. This work provides a very useful source of information for researchers on this subject.

In the present study, the flow of couple stress fluids in expanding and contracting scenarios is investigated.

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

The purpose of this paper is to consider a laminar two-dimensional incompressible flow of an electrically conducting fluid over a moving flat plate with a parallel free stream.

The governing equations are first reduced into self-similar forms and then solved for the numerical solutions by shooting method.

The results are compared with the available studies is some special cases and found in excellent agreement. It is noticed that an increase in the magnetic field strength leads to a decrease in the momentum boundary layer thickness and enhancement in the rate of heat transfer from the plate. It is also observed that temperature and heat transfer from the plate increase when radiation effect is strengthened.

A recently proposed idea of nonlinear radiative heat transfer with Joule heating and viscous dissipation effects is analyzed.

The purpose of this paper is to examine the interaction effects of a transverse magnetic field and slip effects of Casson fluid with suspended nanoparticles over a nonlinear stretching surface. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed.

Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method is employed for its solution. The slope of the linear regression line of the data points is calculated to measure the rate of increase/decrease in the reduced Nusselt number.

The effects of magnetic parameter (0=M=4), Casson parameter (0.1=β<8), nonlinear stretching parameter (0=n=3) and porosity parameter (0=P=6) on axial velocity are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. This study reveals the fact that the Brownian motion parameter and boundary layer thickness have a direct relationship with temperature. Also, Brownian motion and thermophoresis contribute to an increase in the thermal boundary layer thickness.

Despite the immense significance and repeated employment of non-Newtonian fluids in industry and science, no attempt has been made up till now to inspect the Casson nanofluid flow with a permeable nonlinear stretching surface.