Browse
Recent Submissions
Item Open Access Modelling average maximum daily temperature using r largest order statistics: An application to South African data(OASIS, 2018-05-02) Nemukula, M. M.; Sigauke, CastonNatural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000–2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September–April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.Item Open Access On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem(De Gruyter, 2018-05-30) Muzara, Hillary; Shateyi, Stanford; Marewo, Gerald TendayiIn this paper, a bivariate spectral quasilinearization method is used to solve the highly nonlinear two dimensional Bratu problem. The two dimensional Bratu problem is also solved using the Chebyshev spectral collocation method which uses Kronecker tensor products. The bivariate spectral quasi-linearization method and Chebyshev spectral collocation method solutions converge to the lower branch solution. The results obtained using the bivariate spectral quasi-linearization methodwere compared with results from nite di erences method, the weighted residual method and the homotopy analysis method in literature. Tables and graphs generated to present the results obtained show a close agreement with known results from literature.Item Open Access Alternative methods for solving nonlinear two-point boundary value problems(2018-03-18) Ghomanjani, Fateme; Shateyi, StanfordIn this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary di erential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. Stated methods are more easier and applicable for linear and nonlinear problems. Some numerical examples are solved and they are stated the accurate findings.Item Open Access Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction(De Gruyter, 2017-11-27) Shateyi, Stanford; Marewo, Gerald T.We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.