Open Access Method Article

A Mathematical Model for Estimating the Ideal Number of Outsource Academic Staff for Private Universities in Nigeria

Osatohanmwen Enagbonma, Augustine A. Osagiede

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/39675

We developed a model for determining the ideal number of outsourcing academic staff in privately owned universities in Nigeria. The method takes National Universities Commission (NUC) guideline on staff regulation into consideration. The estimated ideal number of outsourcing academic staff will complement the available academic staff so as to meet the staff-mix by rank ratio stipulated by the NUC.

Open Access Original Research Article

Conjugate Effects of Viscous Dissipation and Dependent Viscosity on Natural Convection Flow over a Sphere with Joule Heating and Heat Conduction

Md. M. Alam, Ruhul Imran, Sumita Ghosh, Raihanul Haque

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2018/39155

In the present paper, the effect of viscous dissipation and dependent viscosity on free convection flow over a sphere has been investigated. Joule heating and heat conduction over a sphere are considered as well in this investigation. With a goal to attain similarity solutions of the problem being posed, the developed equations are made dimensionless by using suitable transformations. The non-dimensional equations are then transformed into non-linear equations introducing a non- similarity transformation. The resulting non-linear similar equations together with their corresponding boundary conditions based on conduction and convection are solved numerically by using the finite difference method along with Newton’s linearization approximation. The numerical results detailing the velocity profiles, temperature profiles, skin friction coefficient and the local heat transfer coefficient are shown both in graph and tabular forms for the different values of the parameters associated with the problem.

Open Access Original Research Article

Conservation Properties of the Trapezoidal Rule for Linear Transient Electromagnetics

Arup Nandy, C. S. Jog

Journal of Advances in Mathematics and Computer Science, Page 1-26
DOI: 10.9734/JAMCS/2018/39632

The Time Domain Finite Element Method (TDFEM) has been used extensively to solve transient electromagnetic radiation and scattering problems. But in most implementations so far, vector basis functions have been used to discretize the field variables. In multiphysics simulations that involve coupling the electromagnetic equations with structural or fluid flow equations, nodal finite elements can provide a unified data structure for a monolithic coupled formulation. With such multiphysics simulations in view, in this work we develop a time-stepping strategy to model electromagnetic radiation and scattering within the nodal finite element framework. Although conservation of energy is well-known, we show in this work that there are additional quantities that are also conserved in the absence of loading. We then show that the developed time-stepping strategy (which is closely related to the trapezoidal rule that is widely used for solving linear hyperbolic problems) mimics these continuum conservation properties either exactly or to a very good approximation. Thus, the developed numerical strategy can be said to be ‘unconditionally stable’ (from an energy perspective) allowing the use of arbitrarily large time-steps. The developed method uses standard elements with Lagrange interpolation functions and standard Gaussian quadrature. We demonstrate the high accuracy and robustness of the developed method for solving both interior and exterior domain radiation problems, and for finding the scattered field from conducting and dielectric bodies.

Open Access Original Research Article

Modeling the Autocorrelated Errors in Time Series Regression: A Generalized Least Squares Approach

Emmanuel Alphonsus Akpan, Imoh Udo Moffat

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/JAMCS/2018/39949

This study considered Gross Domestic Product (N’ Billion) as the dependent variable (denoted by Yt),  the Money Supply (N’ Billion) as the independent variable (denoted by X1t ) and the Credit to Private Sector as another independent variable (denoted by X2t). The data were obtained from the Central Bank of Nigeria Statistical Bulletin for a period ranging from 1981 to 2014. Each series consists of 34 observations. The study aimed at applying the generalized least squares to overcome the weaknesses of ordinary least squares to ensure the efficiency of the model parameters, unbiased standard errors, valid t-statistics and p-values, and to account for the presence of autocorrelation. Based on ordinary least squares fitted regression model, our findings revealed that X1t and X2t contributed significantly to Yt and were able to explain about 67.95% of the variance in Yt. However, the diagnosis of the fitted regression model using Breusch and Godfrey test, ACF, and PACF showed that the residuals are correlated, hence the need for generalized least squares. Further findings from the results of generalized least squares estimation revealed that their estimates are better and that the additional information in the error terms (autocorrelation) could be explained and captured by AR (2). Thus, it could be deduced that generalized least squares provides better estimates than the ordinary least squares and also accounts for autocorrelation in time series regression analysis.

Open Access Review Article

A Self-Starting Five-Step Eight-Order Block Method for Stiff Ordinary Differential Equations

D. Raymond, J. Z. Donald, A. I. Michael, G. Ajileye

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/JAMCS/2018/18909

This paper examines the implementation of a self-starting five-step eight-order block method with two off-grid for stiff ordinary differential equations using interpolation and collocation procedures. The predictor schemes are then expanded using Taylor’s series expansion. Multiple numerical integrators were produce and arrived at a discrete scheme. The discrete schemes are of uniform order eight and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for stiff initial value problem for ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.