The study investigated teacher knowledge of error analysis in differential calculus. Two teachers were the sample of the study: one a subject specialist and the other a mathematics education specialist. Questionnaires and interviews were used for data collection. The findings of the study reflect that the teachers’ knowledge of error analysis was characterised by the following assertions, which are backed up with some evidence: (1) teachers identified the errors correctly, (2) the generalised error identification resulted in opaque analysis, (3) some of the identified errors were not interpreted from multiple perspectives, (4) teachers’ evaluation of errors was either local or global and (5) in remedying errors accuracy and efficiency were emphasised more than conceptual understanding. The implications of the findings of the study for teaching include engaging in error analysis continuously as this is one way of improving knowledge for teaching.

This work proposes a numerical approach to model 2D pollutant dispersion in a canal using the famous advection-reaction diffusion equations. The advection-dispersion equation model describes transport and diffusion problems as seen in mixing conservative, nonbuoyant pollutants deposited into a stream or canal. The canal consisted of a narrow channel that allows water inflow through an entry opening and outflow through an exit opening. We obtain stability conditions for finite difference schemes and show the existence and uniqueness of solutions for the finite element method. The simulations show that the concentration of pollutants in the canal is controlled by the divergence term and increases in the direction of fluid flow.

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The nonlinear Schrödinger equation in one-dimensional coordinate is investigated numerically by employing explicit and implicit finite difference methods. It is shown that the explicit method is conditionally stable, and the condition for stability, which is a function of the time step and spatial step size, or several grid points are obtained. It is also shown that the implicit scheme is unconditionally stable and results in a tridiagonal matrix at each time level as a function of the nonlinear term. The effects of dispersion and nonlinearity concerning the time and space steps are also investigated. The validity of our scheme is established by reproducing some existing results on the constant-coefficient nonlinear Schrödinger equation. The schemes are then extended to study the variable coefficient equation, which has a growing interest and applications in many areas of nonlinear science.

Numerical simulation of the wound healing behaviour by considering the coupled reaction-diffusion, transport and viscoelastic system is vital in investigating the mechanical stress field induced by cell migration. In this work, numerical simulation is viewed in three-dimensional space during a time course of wound healing. Over the years, many authors have developed two-dimensional mathematical models of wound healing, as supported by the background in the introduction below. But we know that a three-dimensional case realistically captures the tissue deformations. The two-dimensional simulation is restricted to observing the motion in two directions only. Hence, the interest is in the three-dimensional case. Therefore, to our knowledge, this is the first article to consider the numerical simulation of the coupled reaction-diffusion, transport and viscoelastic system during wound healing in a three-dimensional environment. Firstly, the two-dimensional evolution of wound healing is developed to compare our results with published data. Then the work is extended to three-dimensional wound healing, which is the main focus.