PhD work: Currently working on my PhD (Project 2020).
We focus on “quasi-linear” problems, which are formed of a linear and nonlinear components (L and N, respectively) so that L(u) + N(u) = f. We seek to compare existing methods for finding solutions to various quasi-linear problems, attempting to quantify their accuracy, convergence, and stability properties. We also seek to introduce and develop new iterative methods and apply them to practical-world problems.
MSc work: Dissertation
Our research was based on using computational methods (multistage spectral relaxation method and ode-45) on the HIV infection model with Tat and Ssu72 proteins. These two proteins were shown to work hand in hand in activating the latently infected CD4+ T cells. We wanted to know how much numbers of copies of these proteins are needed for activation and eradication of the virus in an infected individual. Our research showed that with 30-40 copies of each protein the virus can be almost if not eradicated completely. Some of the potholes are left to be covered in future.