Circular Hydraulic Jump

• Have a running 2d code for the CHJ that simulates experimental settings.

• produce some figures and data from the simulation and their experimental counterparts.

Algebraic condition for A-stability for general linear methods

• After verifying that the A-stability proposed definition is in fact correct, Yousef hopes to be able to relate the structure of GLMs to the control theory settings used by Scherer and Wendler 1994. If done, the proof will be a straightforward application of the positive real lemma.

Global search for high-order explicit Runge-Kutta methods.

• Hopefully have a 9th-order method with fewer than 15 stages in rational forms. Yousef doubts that we’ll be able to find the 10th order method given how difficult in baron it is to satisfy 486 OCs (let alone 1205 for order 10); unless we have another more efficient solver.

Nonexistence of A-stable DIRK method with positive coefficients of order higher than 3.

• Discuss how to use MATHEMATICA with Lajos Lóczi to help prove this conjecture.