On the Computation of Blow-up Solutions for Semilinear ODEs and Parabolic PDEs

We introduce an adaptive numerical method for computing blow-up solutions for ODEs and well-known reaction-diffusion equations. The method is based on the implicit midpoint method and the implicit Euler method. We demonstrate that the method produces superior results to the adaptive PECE-implicit method and the MATLAB solver of comparable order

Transport as a servant of trade and its cross-border challenges : a case of Swaziland and the newly introduced immigration laws by the South African government

The movement of goods and services as well as people is usually through road and rail transportation, especially in the Southern African Development Community (SADC). Swaziland is a landlocked country with its economy heavily dependent on trade with other regions and countries. The fact that Swaziland is a landlocked country means that its trade relations are not only dependent on transport but also on cross-border regulations with the countries it shares its borders with. Regional integration also plays a key role in the countries trade associations. The republic of South Africa happens to be Swaziland?s major trading partner. New immigration laws have been introduced by the Republic of South Africa and they came into effect early 2014. This paper uses Swaziland as a case study to reflect on the issues of new immigration laws, the effect they will have on regional integration which could be achieved through transportation, contribution to already existing cross-border challenges and most importantly, their impact on trade issues, which in this case is the movement of goods and services across borders, as well as the coming in and out of people. Transportation refers to all modes used for the movement of goods, services and people, this includes non-motorised transport, but particular attention will be paid to road transportation. Laws tend to be a hindrance to the flow of goods and service therefore slowing down the economy, however regulation is needed. Their implementation thereof, should be in a manner that will not worsen trade and the transportation system of one country.Paper presented at the 34th Annual Southern African Transport Conference 6-9 July 2015 "Working Together to Deliver - Sakha Sonke", CSIR International Convention Centre, Pretoria, South Africa.The Minister of Transport, South AfricaTransportation Research Board of the US

Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations

How Swaziland and South Africa can integrate to improve their economic status through transportation : road and rail transportation

Paper presented at the 33rd Annual Southern African Transport Conference 7-10 July 2014 "Leading Transport into the Future", CSIR International Convention Centre, Pretoria, South Africa.Integration may be said to be a key element in most countries’ development policies, for example, South Africa’s “African agenda” which part of its goals were to contribute towards the SADC Common Agenda, in hope for integration of multi and bilateral action programs. Integration may be defined as the process of attaining close and seamless coordination between several organisations, systems etc. There are different forms of integration; regional, system, economic integration to name but a few. The latter form of integration can be defined as a process and as a state of affairs. Regarded as a process, it encompasses measures designed to abolish discrimination between economic units belonging to different national states (Balaso, 1961). Economic integration transpires at a time when two or more nations carry out policies that result in bigger mutual interdependence. It follows that if such countries (those that are to integrate) stem from a single regional or regional integration activities, they are to be termed as ‘regional economic integration.’ (Negasi, 2009) According to a report by the World Bank in 2011, both South Africa and Swaziland were ranked as 3rd world countries (by GNI per capita), with the former classified as upper middle income country whilst Swaziland was classified as a lower middle income state. Both countries are part of the Southern African Development Community. The true objective of SADC is full economic integration of the Southern Africa region and trade liberalization. South Africa and Swaziland already have forged links with each other through the above mentioned organization. “Swaziland and South Africa, both developing 3rd world countries, entered into bilateral and multilateral agreements governing or touching on transport and logistics related issues (Mpata et.al, 2004). Included in these agreements are the SACU Arrangements and the SADC Transport and Communications Protocol.” Since the two countries are already part of an organization which part of its objective is full economic integration, this essay will look at how to link the two countries' development objectives and align them through transport.This paper was transferred from the original CD ROM created for this conference. The material was published using Adobe Acrobat 10.1.0 Technology. The original CD ROM was produced by CE Projects cc. Postal Address: PO Box 560 Irene 0062 South Africa. Tel.: +27 12 667 2074 Fax: +27 12 667 2766 E-mail: [email protected]

Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems

We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method

The role of horizontal philanthropy in mitigating the impacts of HIV/AIDS in rural areas : a case study of Mathulini Rural Area.

Masters in Development Studies. University of KwaZulu-Natal, Howard College 2014.This Masters dissertation documents the results of a qualitative research study on how horizontal giving lessens the impacts of HIV/AIDS in the rural Mathulini area of KwaZulu-Natal, South Africa. The main objective of this research study was to understand the role and importance of horizontal philanthropy (giving occurring amongst families, friends and within communities) in mitigating the impact of HIV/AIDS in a rural community. The study was conducted in the Mathulini rural area of KwaZulu-Natal, with a focus on a community based organisation, the Mathulini Women’s Group. The thesis uses the theory of horizontal philanthropy to investigate the role of philanthropy in rural areas, especially towards reducing HIV/AIDS impacts within these communities. In this research an understanding of horizontal philanthropy from a South African perspective was first put forward. Using participant observation and interview research methods, the study concludes that giving and philanthropy form a large part of South African tradition and culture, and also impact positively on the country’s citizens. Based on an understanding of horizontal philanthropy, the study then reflects the way in which people from poor and marginalised settings engage in horizontal philanthropy as means of helping each other on a daily basis. It highlights the role of horizontal philanthropy in mitigating the impact of HIV/AIDS within the rural communities. This study contributes to the nascent literature on African indigenous philanthropies

Nonlinear nanofluid flow over heated vertical surface with sinusoidal wall temperature variations

The nonlinear density temperature variations in two-dimensional nanofluid flow over heated vertical surface with a sinusoidal wall temperature are investigated. The model includes the effects of Brownian motion and thermophoresis. Using the boundary layer approximation, the two-dimensional momentum, heat, and mass transfer equations are transferred to nonlinear partial differential equations form and solved numerically using a new method called spectral local linearisation method.The effects of the governing parameters on the fluid properties and on the heat and nanomass transfer coefficients are determined and shown graphically

Prunier d'Afrique (Sclerocarya birrea)

Conservation and sustainable use of genetic resources of priority food tree species in sub-Saharan AfricaConservation et utilisation durable des ressources génétiques des espèces ligneuses alimentaires prioritaires de l'Afrique subsaharienneLa publicación de esta hoja divulgativa ha sido financiada con la acción complementaria nº AC-2008-00050-00-00, titulada "Publicación de hojas divulgativas: Uso y gestión sostenible y conservación de especies forestales para la alimentación (ELA) en Africa Subsahariana" solicitada por el Centro de Investigación y Tecnología Agroalimentaria de Aragón (CITA), investigador responsable: Eduardo Notivo

On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations

We make use of an adaptive numerical method to compute blow-up solutions for nonlinear ordinary Volterra integrodifferential equations (VIDEs). The method is based on the implicit midpoint method and the implicit Euler method and is named the implicit midpoint-implicit Euler (IMIE) method and was used to compute blow-up solutions in semilinear ODEs and parabolic PDEs in our earlier work. We demonstrate that the method produces superior results to the adaptive PECE-implicit Euler (PECE-IE) method and the MATLAB solver of comparable order just as it did in our previous contribution. We use quadrature rules to approximate the integral in the VIDE and demonstrate that the choice of quadrature rule has a significant effect on the blow-up time computed. In cases where the problem contains a convolution kernel with a singularity we use convolution quadrature