Welcome to the blog I'll be keeping while participating in the 2018 Fields Undergraduate Summer Research Program . The program is through the Fields Institute for Research in Mathematical Sciences, which is on the campus of the University of Toronto in Ontario, Canada. I will be participating in Project 5 along with other students from around the world. From the above website: "This project is about the methods used for numerical simulations of both exo-planetary systems and our own Solar System. Having fast and accurate numerical tools to perform such simulations is crucial if we want to understand the dynamical architecture of these systems." My understanding of the project is as follows: we'll be working on a project that involves solving complicated equations (higher-order differential equations, specifically). These equations are complicated enough that we can't solve them using our nice standard techniques. Because of these complexities, we turn...