Parabolic PDE, Explicit vs Implicit. This project focused on parabolic partial differential equations, explicit vs. implicit. David discussed in great detail the benefits of using both explicit and implicited PDE's. Explicit is more accurate when stable for the hyperbolic assuming the Courant number is 1. Explicit's temporal error does better at canceling spatial error than implicit's does. Implicit can be used to solve equations whereas explicit can be used to solve for timestep. David displayed many equations on the board and went over a large majority of his project explaining and displaying these equations. Although his research is not quite finished, we all believe that he would make an incredible math teacher.

For details see David's pages