A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages

Moderation and Mediation of an Effective HIV Risk-Reduction Intervention for South African Adolescents

Let Us Protect Our Future is a sexual risk-reduction intervention for sixth-grade adolescents in South Africa. Tested in a cluster-randomized controlled trial, the intervention significantly reduced self-reported intercourse and unprotected intercourse during a 12-month follow-up period. The present analyses were conducted to identify moderators of the intervention\u27s efficacy as well as, which theory-based variables mediated the intervention\u27s effects. Intervention efficacy over the 3-, 6-, and 12-month follow-up was tested using generalized estimating equation models. Living with their father in the home, parental strictness, and religiosity moderated the efficacy of the intervention in reducing unprotected intercourse. Self-efficacy to avoid risky situations and expected parental disapproval of their having intercourse, derived from Social Cognitive Theory, significantly mediated the intervention\u27s effect on abstinence. This is the first study to demonstrate that Social Cognitive variables mediate the efficacy of a sexual risk-reduction intervention among South African adolescents. --author-supplied descriptio

Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

We propose a block hybrid trigonometrically fitted (BHT) method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs), such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages

What are we measuring? Comparison of household food security indicators in the Eastern Cape Province, South Africa

The development of national food security information systems is constrained by a lack of guidance on which indicators to use. This paper compares food security indicators across two seasons (summer and winter) in one of the most deprived areas of the Eastern Cape province of South Africa. The results show that only anthropometric indicators are sensitive enough to differentiate levels of food insecurity. The lack of consistent classification across indicators means that surveys must use a combination of food consumption and experience of hunger measures backed up by anthropometric measures. Targeting interventions is difficult if the measures cannot be relied on. Further investigation is needed to identify a suite of appropriate indicators for a national information and surveillance system.South African Water Research Commission (WRC Project No. Project K5/2172/4), the South African National Research Foundation (Grant numbers CPR20110706000020, 77053 and 80529), the University of Pretoria’s Institutional Research Theme on Food, Nutrition and Well-being, and the University of Pretoria’s Post-Doctoral Fellowship Programme.http://www.tandfonline.com/loi/gefn202017-09-30hb2016Agricultural Economics, Extension and Rural Developmen

“Ndiyindoda” [I am a man]: theorising Xhosa masculinity

Masculinity studies in South Africa depend on Western gender theories to frame research questions and fieldwork. This article argues that such theories offer a limited understanding of Xhosa constructions of masculinity. Xhosa notions of masculinity are embodied in the concept of indoda, meaning a traditionally circumcised person. This article explores the nuanced meanings of indoda and its relationship to other masculinities, like uncircumcised boys [inkwenkwe] and medically circumcised men. The discussion reveals that indoda is the most “honoured” form of masculinity. A traditionally circumcised individual is regarded as indoda, a real man, irrespective of his sexual orientation or class, and this affords him certain rights and privileges. Inkwenkwe and medically circumcised men embody “subordinate” forms of masculinity and are victims of stigma and discrimination by indoda. This requires us to revisit some Western theories of masculinity which place heterosexual men at the top of a masculine hierarchy and gay men at the bottom. It furthermore requires us to pay attention to the body when theorising Xhosa masculinity, since it is a principal way of “proving” and “defending” Xhosa manhood.IBS

A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems

A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in predictor-corrector form are implemented in block form as simultaneous numerical integrators over nonoverlapping intervals. Numerical results obtained using the proposed block form reveal that the new methods are efficient and highly competitive with existing methods in the literature

Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency