Open Access Original Research Article

Solving Delay Differential Equations Using Reformulated Block Backward Differentiation Formulae Methods

U. W. Sirisena, S. Y. Yakubu

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v32i230139

In this paper, the conventional backward differentiation formulae methods for step numbers k = 3 and 4 were reformulated by shifting them one-step backward to produce two and three approximate solutions respectively, in a step when implemented in block form. The derivation of the continuous formulations of the reformulated methods were carried out through multistep collocation method by matrix inversion technique. The discrete schemes were deduced from their respective continuous formulations. The convergence analysis of the discrete schemes were discussed. The stability analysis of these schemes were ascertained and the P- and Q-stability were also investigated. When the discrete schemes were implemented in block form to solve some first order delay differential equations together with an accurate and efficient formula for the solution of the delay argument, it was observed that the results obtained from the schemes for step number k = 4 performed slightly better than the schemes for step number k = 3 when compared with the exact solutions. More so, on comparing these methods with some existing ones, it was observed that the methods derived performed better in terms of accuracy.

Open Access Original Research Article

A Sharp Estimate of Entropy Solution to Euler-Poisson System for Semiconductors in the Whole Domain

Yanqiu Cheng, Xixi Fang, Huimin Yu

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/jamcs/2019/v32i230140

In this paper, we are concerned with the global existence, large time behavior, and timeincreasing-rate of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. When the adiabatic index γ > 2, the L∞ estimates of artificial viscosity approximate solutions are obtained by using entropy inequality and maximum principle. Then the L∞ compensated compactness framework demonstrates the
convergence of approximate solutions. Finally, the global entropy solutions are proved to decay exponentially fast to the stationary solution, without any assumption on the smallness of initial data and doping profile.

Open Access Original Research Article

An Improved Geo-Textural Based Feature Extraction Vector For Offline Signature Verification

Kennedy Gyimah, Justice Kwame Appati, Kwaku Darkwah, Kwabena Ansah

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v32i230141

In the field of pattern recognition, automatic handwritten signature verification is of the essence. The uniqueness of each person’s signature makes it a preferred choice of human biometrics. However, the unavoidable side-effect is that they can be misused to feign data authenticity. In this paper, we present an improved feature extraction vector for offline signature verification system by combining features of grey level occurrence matrix (GLCM) and properties of image regions. In evaluating the performance of the proposed scheme, the resultant feature vector is tested on a support vector machine (SVM) with varying kernel functions. However, to keep the parameters of the kernel functions optimized, the sequential minimal optimization (SMO) and the least square method was used. Results of the study explained that the radial basis function (RBF) coupled with SMO best support the improved featured vector proposed.

Open Access Original Research Article

New Conditions That Guarantee Uniform Asymptotically Stable and Absolute Stability of Singularly Perturbed Systems of Certain Class of Nonlinear Differential Equations

Ebiendele Peter, Asuelinmen Osoria

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/jamcs/2019/v32i230142

The objectives of this paper is to investigate singularly perturbed system of the fourth order differential equations of the type,       to establish the necessary and  sufficient new conditions that guarantee, uniform asymptotically stable, and absolute  stability of the  system. The Liapunov’s functions were the mathematical model used to establish the main results of this study. The study was motivated by some authors in the literature, Grujic LJ.T, and Hoppensteadt, F., and the results obtained  in this study improves upon their results to the case where more than two arguments was established.

Open Access Original Research Article

Road Network Pre-partitioning Method with Priority for Congestion Control

Hao She, Xingsheng Xie

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/jamcs/2019/v32i230143

Urban traffic congestion seriously affects the traffic efficiency, causing travel delays and resources wasted directly. In this paper, a road network pre-partitioning method with priority for congestion control is proposed to reduce traffic congestion. Traffic flow feature is extracted based on CNN, and the estimated accuracy of intersection reach 95.32% through CNN-SVM model. Subarea congestion coefficient and intersection merger coefficient are defined to expand the control area of congestion coordination. The association and similarity of intersections are considered using spectral clustering for non-congested intersection partitioning. The results show that the congestion priority control partition method reduces a congestion intersection compared to directly using spectral clustering for subarea partition, and reduces the road network congestion coefficient by 0.05 after 30 minutes than directly using spectral clustering, which is an effective subarea partition method.