Katherine has been studying differential equations, an important field of applied Mathematics. Differential equations describe relationships that involve changing quantities, and are used to describe the rate at which they change. For example, differential equations can provide a mathematical description of how planets orbit, or what happens with sub-atomic particles inside atoms, or even biological questions like growth rates. There are several benefits for having an exact or approximate solution of a differential equation. Recently, a technique called the Asymptotic Iteration Method (AIM) was introduced to find exact or approximate solutions to a specific type of differential equations. One of the researchers who introduced AIM is Dr. Nasser Saad, Katherine’s supervisor.
This past summer, Katherine used AIM to solve a more complicated type of differential equations, a system of two differential equations. She re-examined and contributed to the basic theory of AIM. As a consequence of her research, a method of generating exact solutions to this interesting class of differential equations has been introduced.
Student Research