Open Access Method Article

Adaptive Variable Weight Accumulation AVWA-DGM(1,1) Model Based on Particle Swarm Optimization

Lang Yu

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/jamcs/2019/v32i430150

The development of higher education is an extremely important issue. It is the source of the country's technological innovation and the realization of innovation and development, especially in China, where higher education is still at an exploratory stage. Aiming at the shortcoming that the classical DGM (1,1) model accumulates the raw data series with the weight of constant "1", this paper proposes an adaptive variable weight accumulation optimization DGM (1,1) model, abbreviated as AVWA-DGM (1,1) model. Taking the enrollment numbers of postgraduate, master degree, undergraduate and junior college student and undergraduates students in China as numerical examples, the DGM (1,1) model and AVWA-DGM (1,1) model are established to simulate and predict respectively, and the weighted coefficients of AVWA-DGM (1,1) model are optimized and solved by particle swarm algorithm. The results show that the AVWA-DGM(1,1) model has higher simulation and prediction accuracy than the classical DGM(1,1) model in the four numerical examples provided in this paper. It can be seen that the adaptive accumulation of the raw data sequence by the particle swarm optimization algorithm can make the first order accumulation sequence more in line with the requirements of the DGM (1,1) model on the data features, thereby improving the simulation and prediction accuracy.

Open Access Original Research Article

Perturbation Solutions to Fifth Order Over-damped Nonlinear Systems

Harun-Or- Roshid, M. Zulfikar Ali, Pinakee Dey, M. Ali Akbar

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2019/v32i430151

Fifth order over-damp nonlinear differential systems can be used to describe many engineering problems and physical phenomena occur in the nature. In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to investigate the solution of a certain fifth order over-damp nonlinear systems and desired result has been found. The implementation of the presented method is illustrated by an example. The first order analytical approximate solutions obtained by the method for different initial conditions show a good agreement with those obtains by numerical method.

Open Access Original Research Article

Solving Directly Second Order Initial Value Problems with Lucas Polynomial

A. O. Adeniran, I. O. Longe

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/jamcs/2019/v32i430152

Aims/ Objectives: This   paper   presents    a  one step  hybrid  numerical  scheme  with one off grid  points   for solving directly the general second order initial value problems.
Study Design: Section one which is the introduction, give a brief about initial value problem. In the next section derivation of one step hybrid scheme is considered. Section Three provides  the  analysis  of  the  scheme,  while numerical implementation of the scheme and conclusion are in Sections four and five respectively.
Methodology: The  scheme  is  developed  using  collocation  and  interpolation  technique  invoked   on   Lucas polynomial.
Results: The proposed scheme is consistent, zero stable and of order four  and  can  estimate  the  approximate solution at both step and o step points simultaneously by using variable step size.
Conclusion: Numerical results are given to  show  the  efficiency  of  the  proposed  scheme  over  some  existing schemes of same and higher order[ [1],[2], [3],[4], [5], [6]].

Open Access Original Research Article

Calculation and Analysis of the Amber Interval in Traffic Flow

Meng Xinyu, Zhao Jian, Zhang Wei, Meng Zhaoping

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v32i430153

According to the relationship between the speed of vehicle and the amber light, we establish the differential equation model of the amber light duration. And based on the relevant conditions given in the title, three differential equation models of amber light duration under different conditions are obtained. Considering the traffic condition and driver's habit, we calculate a value that is most suitable to the actual demand. The sensitivity and stability of the model and its related factors are analyzed. We improve the model for the problem of difficult area.

Open Access Review Article

Geometrical Properties and Exact Solutions of Three (3+1)-Dimensional Nonlinear Evolution Equations in Mathematical Physics Using Different Expansion Methods

A. R. Shehata, Safaa S. M. Abu-Amra

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/jamcs/2019/v32i430149

In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics.

In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics.