In this paper, we suggest collocation method depending on Cubic trigonometric B-spline (CuTBS) approach based on finite difference scheme to solve the modified regularized long wave equation. The single solitary wave motion was studied using the proposed method; thus the accuracy and efficiency of the suggested method were computed from the L ₂, L _∞ norms. Also, the von-Neumann method was used to study the linear stability analysis. The obtained results through the tested two problems exhibited that, the method is an effective numerical scheme to solve Modified Regularized Long Wave equation (MRLW).

In this paper, new transform with fundamental properties are presented. The new transform has many interesting properties and applications which make it rival to other transforms. Furthermore, we generalize all existing differentiation, integration, and convolution theorems in the existing literature. New results and new shifting theorems are introduced. Finally, comprehensive list of this transforms of functions will be providing.

Hookah is a tobacco product that is gaining popularity in the United States and other countries, particularly among the youth. In this paper, we examine the perception of health risks of different types of tobacco use in comparison to hookah use among 671 participants respond to a survey conducted in Detroit Metropolitan Area, Michigan who never smoke or smoke “cigarette, hookah, both cigarette and hookah”; and determine whether smoking status influenced the perceived health risks of hookah smoking when compared to other forms of tobacco use. The survey had 43 questions including questions about demographics, socioeconomic status, health care, etc. All statistical analyses were done using SPSS version 22. This study found that 44.1% of the participants believed that hookah was less harmful than each of the other tobacco products studied. Approximately 26% of cigarette smokers are likely to smoke hookah also. These findings emphasize the importance of spreading awareness about the health risks associated with hookah smoking and implementing strict laws for showing tobacco-related warnings in hookah advertisements and on the packets of hookah accessories given the increasing popularity of hookah, especially among the youth, in the United States.

This paper presents a new transform method to solve partial differential equations, for finding suitableaccurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions. Finally, all algorithms in this paper are implemented in MATLAB version 7.12.

The aim of this paper is to design feed forward neural network for solving second-order singular boundary value problems in ordinary differential equations. The neural networks use the principle of back propagation with different training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Two examples are considered to show that effectiveness of using the network techniques for solving this type of equations. The convergence properties of the technique and accuracy of the interpolation technique are considered.

The aim of this paper is to evaluate the rate of contamination in soils by using accurate numerical method as a suitable tool to evaluate the concentration of heavy metals in soil. In particular, 2D –interpolation methods are applied in the models of the spread the metals in different direction.The paper illustrates the importance of the numerical method in different applications, especially nvironment contamination. Basically, there are many roles for approximating functions. Thus, the approximating of function namely the analytical expression may be expressed; the most common type being is polynomials, which are the easy implemented and simplest methods of approximation. In this paper the divided difference formula is used and extended in two dimensions (2D) to evaluate the concentration of metals in soil to estimate the rate of contamination in Baghdad city, Iraq.