Piecewise Analytic Method VS Runge-Kutta Method (Comparative Study)

Even though Runge-Kutta (RK) method is the most used by scientists and engineers, it is not the most powerful method. In this paper, a comparative study between Piecewise Analytic Method (PAM) and RK methods is achieved. The result of comparative study shows that PAM is more powerful and gives results better than RK Methods. PAM can be considered as a new step in the evolution of solving nonlinear differential equations.

Fractional modeling for prey and predator problem by using optimal homotopy asymptotic method

In this paper, a fractional-ordered prey and predator population model is introduced and applied to obtain an approximate solution with help of optimal homotopy asymptotic method (OHAM). Some plots for populations of the prey and the predator versus time are presented to show the efficiency and the accuracy of the method and confirm that the method is straightforward as well. The fractional derivatives are described in the Caputo sense.

Uniqueness of approximate solutions to the Gelfand Levitan equation

This brief paper considers a potential issue of using iterative solutions for the Gelfand-Levitan equation. Iterative solutions require approx-imation methods and this could lead to a loss of uniqueness of solutions. The calculations in this paper demonstrate that this is not the case and that uniqueness is preserved.

Orthonormal Bernstein polynomials for Volterra integral equations of the second kind

The purpose of this research is to provide an effective numerical method for solving linear Volterra integral equations of the second kind. The mathematical modeling of many phenomena in various branches of sciences lead into an integral equation. The proposed approach is based on the method of moments (Galerkin- Ritz) using orthonormal Bernstein polynomials. To solve a Volterra integral equation, the ap-proximation for a solution is considered as an expansion in terms of Bernstein orthonormal polynomials. Ultimately, the usefulness and extraordinary accuracy of the proposed approach will be verified by a few examples where the results are plotted in diagrams, Also the re-sults and relative errors are presented in some Tables.

Stability analysis of a mathematical model for awareness initiatives on registration of persons in Kenya

In this paper, we discuss stability analysis of a mathematical model of awareness initiatives in registration of persons in Kenya. Using Ordinary Differential Equations, a mathematical model to compare the efficacy of print media, electronic media and word-of-mouth media in disseminating registration information is developed. Positivity and boundedness of solutions is established to ensure that the model is mathematically meaningful. The Basic Reproduction number R0 is derived using the Next Generation Matrix. We present both awareness free equilibrium and the maximum awareness equilibrium. Stability analysis of the model shows that Awareness free equilibrium is both locally and globally asymptotically stable when R0 < 1 hence no spread of awareness and unstable when R0 > 1 while MAE is locally asymptotically stable when R0 > 1 indicating spread of information in the population.

Voting method based on approval voting and arithmetic mean

Voting plays a vital role in any society. Indeed the votes involve decision making especially and the more in the decision of group. Thanks to the opinions expressed by a group of people, an opinion representing the preference of the group is determined. But most often some voting methods seem to distance the result from a vote of the general opinion. The study of voting methods is based on the theory of social choice. For several years, in the literature on the theory of social choice, many theorists have contributed trying to find a representative voting method.It seems that there is no totally satisfactory way of voting.Thus we have tried, through this article, to design a voting method based on approval voting and the arithmetic mean that leads to goodcompromise results.In contrast to the other methods, the new method takes into account the choice of each voter and allows to obtain a result which represents the choice of the majority of the voters.

New robust-ridge estimators for partially linear model

This paper considers the partially linear model when the explanatory variables are highly correlated as well as the dataset contains outliers. We propose new robust biased estimators for this model under these conditions. The proposed estimators combine least trimmed squares and ridge estimations, based on the spline partial residuals technique. The performance of the proposed estimators and the Speckman-spline estimator has been examined by a Monte Carlo simulation study. The results indicated that the proposed estimators are more efficient and reliable than the Speckman-spline estimator.

Global stability for a discrete SIR epidemic model with delay in the general incidence function

In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h > 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, the endemic equilibrium is globally asymptotically stable.

Solution of a system of differential equations with constant coefficients using in-verse moments problem techniques

It is known that given a system of simultaneous linear differential equations with constant coefficients you can apply the Laplace method to solve it. The Laplace transforms are found and the problem is reduced to the resolution of an algebraic system of equations of the determining functions, and applying the inverse transformation the generating functions are determined, solutions of the given system. This implies the need to know the analytical form of the inverse transform of the function. In this case the initial conditions consist in knowing the value that the generating function and its derivatives takes at zero. A generalization of this method is proposed in this work, which is to define a more general integral operator than the Laplace transform, the initial conditions consist of Cauchy conditions in the contour. And finally, we find a numerical approximation of the inverse transformation of the generating functions, using the techniques of inverse moment problems, without being necessary to know the analytical form of the inverse transform of the function.

A comparison study of NoSQL document-oriented database system

By increasing data generation at these day, requirement for a sufficient storage system are strongly needed by stakeholders to store and access huge number of data in efficient way for fast analysis and decision. While RDBMS cannot deal with this challenge, NoSQL has emerged as a solution to address this challenge. There have been plenty of NoSQL database engine with their categories and characteristics, especially for document-oriented database. However, it makes a confusion for the system developer to choose the appropriate NoSQL database for their system. This paper is our preliminary report to provide a comparison of NoSQL databases. The comparison is based on performance of execution time which is measured by building a simple program. This experiment was done in our local cluster by exploiting around 1 million datasets. The result shows that RDB has better performance than CDB in terms of execution time.