In this article, the two dimensional Advection- Diffusion equation has been solved by two finite difference techniques. In the first technique an Alternating Direction Implicit scheme (ADI) is used, this technique is a second order accurate in time and space. In the second technique a Crank Nicolson (CN) method is adapted. This method is known to be of order two in space and time, implicit in time, unconditionally stable and has higher order of accuracy. The numerical results are compared with the analytic solution to illustrate the performance and the efficiency of the methods.
Background: The general wellbeing of children has become an issue of increasing concern and it has been a major problem in developing countries like Ethiopia.
Objective: This study is an attempt to identify the determinants of weight for age status of children in Ethiopia using data collected during the Ethiopia Demographic and Health Survey (EDHS) in 2011.
Design: The sampling technique employed was multistage stratified cluster sampling.
Results: Analysis of the study revealed that 29.2% of children under 5 years of age are underweight. Results of the multiple binary logistic regressions showed that region of residence, age of the child, educational status of mothers, preceding birth interval, availability of electric power and sex of child are the most important determinants of weight for age status of children. Among the multilevel models, the random intercept model best fitted the data than the others considered in the analyses. The variance of random component related to the intercept term indicated variations in childhood underweight among the regions. Amhara, Somali, Ben-Gumuz, Tigray and Afar regional states were more likely to have underweight children. Although there is region- wise disparity in children weight-for-age status, it is observed that children living in rural parts of the country are at higher risk of being underweight.
Conclusion: Primary health care and nutrition programs which would fit the features of each region be designed and implemented to safeguard children from nutritional deficiency resulting in underweight children.
A deterministic model was developed to describe the two dominant tribal coalition based voting bloc (A and B) and other tribes (C). The first order nonlinear ordinary differential equations were deduced using predator-prey equations. The system was established to lie in feasible region. The coalition free steady state was determined. The conditions necessary for local stabilities of steady states were determined using Routh-Hurwitz criteria for stability. The condition necessary for global stability of steady state were determined using Lyapunov function. The estimated numerical bound of the registered voters was obtained as 27871013. Numerical simulation was carried out using 2013 general election scenario.
In this article, we introduced the concept of (F, f)-contraction and the concept of generalized (F, f)-contractions on a Gp-metric space. Furthermore, we obtained some common fixed point results for two Banach pairs of mappings which satisfy (F, f)-contraction and the generalized (F, f)-contractions. The presented theorems generalize known results in the literature. We also provide examples to illustrate the usability of our results presented herein.
A class of more general HIV infection models with time delay is proposed based on some important biological meanings. The e ect of time delay on stability of the equilibria of the infection model has been studied. Sensitivity analysis is performed on a delay differential equation model for HIV- 1 infection model that suggests the parameter value has a major impact on the model dynamics. In this paper, the variational iteration method is applied to DDE model for HIV-1 infection model with two discrete delays. Using VIM, it is possible to nd the exact solution or an approximate solution of the proposed problem. This technique provides a sequence of functions which converges to the exact solution of the problem. We also compare the performance of the method with that of a particular Adomain decomposition method. These results reveal that the proposed method is very eff ective and simple to perform.
In the most of works, related to the thermal stability of superconductors maintained by cryogenics, the authors consider the milieu as a threadlike wire of an infinite length. The study of this unidimensional geometric milieu is characterized by some quantities of installation, the Stekly parameter and the Biot number in particular. After proposition of a new non-dimensionalization analysis based on the injection of some floating parameters, our main objective has been to lead to a generalization of these parameters in order to obtain a valid writ for any geometric dimension. The Stekly parameter presents the quality of cooling. We can, according to its value, affirm if the Joule effect is well controlled or if there is a degradation risk of installation. The Biot number reflects the relation between convective and conductive flux. The combination of these parameters helps to analyse the quality of alloy, as well the geometric data of milieu. During this work, we have been able to propose an equation that governs the thermal state of a three-dimensional superconductor.
The main aim of this paper is to propose a numerical integration method using polynomial interpolation that provides improved estimates as compared to the Newton-Cotes methods of integration. The method is an extension of trapezoidal rule where the Lagrange interpolation is employed when fitting polynomials after segmentation. We proved that the proposed numerical integration method using polynomial interpolation provided an improved formula for numerical integration. The proposed method using polynomial interpolation gave better estimates as compared to some Newton-Cotes methods of integration.