About Dr Justin Prentice
Justin Prentice is currently a senior lecturer in the Department of Applied Mathematics. He obtained BSc and MSc (Physics) degrees from the University of the Witwatersrand, BSc(Hons) degrees in Physics and Applied Mathematics and an MSc (Applied Mathematics) from RAU. He graduated in the degree of PhD (Physics) in 1999, and PhD (Applied Mathematics) in 2004, both at RAU.
His MSc in Physics, titled Electrical Resistivity and Magnetic Susceptibility of (Ce,La)PdSb, was a project in the field of experimental magnetism under the supervision of Prof P de V du Plessis.
His MSc in Applied Mathematics, titled A Numerical Method based on Runge- Kutta and Gauss-Legendre integration for solving initial-value problems in ordinary differential equations, was a project in the field of numerical analysis under the supervision of Prof CM Villet.
His PhD in Physics was based on a thesis titled The development of a one-dimensional simulation of thin film photovoltaic devices and an investigation into the properties of a-Si:H solar cells. This project was part of the photovoltaics research programme in the Physics department, and was supervised by the late Prof R Swanepoel and Prof V Alberts.
His PhD in Applied Mathematics was titled Incorporation of the first derivative into the linear training of a radial basis function neural network for approximation via strict interpolation. This project concerns the use of RBF networks in function approximation, such that the first derivative of the objective function is used in the approximation. The project was supervised by Prof W-H Steeb.
Papers and conferences
Highest qualification PhD (Physics, RAU), PhD (Applied Math., RAU)
Field(s) of research
Numerical Analysis (post 2003), Photovoltaic Simulation (pre 2003)
Lecturing: Modules with short description
APM1A & APM1B – Introduction to Statics & Dynamics (1st year courses, applications of vector algebra and vector calculus)
APM2A – Introduction to Differential Equations (2nd year course, solution techniques for a variety of differential equations)
APM2B – Introduction to Numerical Analysis (2nd year course, study of various numerical methods)
APM3A – Variational Calculus and Optimization (3rd year course, calculus of variations, optimization methods and neural networks)
APM0127 & APM0137 – Numerical Analysis A & B (Honours courses, advanced study of various topics in Numerical Analysis)
List of publications (20 most recent)
JSC Prentice, Range and Domain Partitioning in Piecewise Polynomial Approximation, Studies in Mathematical Sciences, 2, 2 (2011) 67-77
JSC Prentice, Stepsize selection in explicit Runge-Kutta methods for moderately stiff problems, Applied Mathematics (p-ISSN: 2152-7385, e-ISSN: 2152-7393), 2, 6 (2011) 711-717
JSC Prentice, Absolute and relative error control in composite interpolatory quadrature: the CIRQUE algorithm, Journal of Mathematics Research, 3, 3 (2011) 63-72
JSC Prentice, Numerical approximation of the Fermi-Dirac integral of order ½ by means of composite Gauss-Legendre quadrature, International Journal of Numerical Methods and Applications, 5, 1 (2011) 17-29
JSC Prentice, Relative Error Control in Bivariate Interpolatory Cubature, arXiv.org (Cornell University Library), 2011, 14p, [arXiv:1110.2324]
JSC Prentice, Runge-Kutta Methods: Local error control does not imply global error control, Journal of Pure and Applied Mathematics: Advances and Applications, 6, 1 (2011) 71-84; also at [arXiv:1110.5728]
JSC Prentice, Relative Global Error Control in the RKQ Algorithm for Systems of Ordinary Differential Equations, Journal of Mathematics Research, 3, 4 (2011) 59-66
JSC Prentice, Nyström Methods in the RKQ Algorithm for Initial-value Problems, arXiv.org (Cornell University Library), 2011, 7p, [arXiv:1110.6749]
JSC Prentice, Global Error Control in the Runge-Kutta Solution of a Hamiltonian System, arXiv.org (Cornell University Library), 2011, 12p, [arXiv:1111.6996]
JSC Prentice, Relative Error Control in Finite-Difference Solutions of Two-Point Boundary-Value Problems, Applied Mathematical Sciences, 6, 19 (2012) 901-911
JSC Prentice, Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson’s Equation, International Journal of Mathematical Education in Science and Technology, 43, 5 (2012) 684-694
JSC Prentice, Global Error Control in a Lotka-Volterra System using the RKQ Algorithm, Journal of Mathematical and Computational Science, 2, 2 (2012) 413-424
JSC Prentice, Efficiency of the RKQ Algorithm, Applied Mathematical Sciences, 6, 52 (2012) 2587-2591
JSC Prentice, Global Error and Stepsize Selection in Moderately Stiff Problems, Applied Mathematical Sciences, 6, 52 (2012) 2593-2597
JSC Prentice, Error-induced Stiffness in the Runge-Kutta Solution of a Lotka-Volterra System, Applied Mathematical Sciences, 6, 52 (2012) 2599-2604
JSC Prentice, Event Location and Global Error in Runge-Kutta Methods, Applied Mathematical Sciences, 6, 64 (2012) 3163-3167
JSC Prentice, The Relative Efficiency of Quenching and Reintegration for Global Error Control in Runge-Kutta Methods, Journal of Mathematical and Computational Science, 2, 4 (2012) 880-888
JSC Prentice, Numerical Differentiation – A General Purpose Algorithm, International Journal of Mathematical Education in Science and Technology, 44, 1 (2013) 116-122
JSC Prentice, Error in Runge-Kutta Methods, International Journal of Mathematical Education in Science and Technology, 44, 3 (2013) 434-442
JSC Prentice, False convergence in the nonlinear shooting method, Journal of Mathematical and Computational Science, 5, 4 (2015) 454-461