In the summer of 2016, Ying Zhang worked with me on the computation of matrix exponentials. She studied properties of matrix exponentials, the connection with solutions of ODEs, as well
as the computational method.

During the same period, Benjamin Bowman worked with me on embedded Runge-Kutta
method for solving ODEs. One simple question that we tried to answer is the following: Given the family of second order Runge-Kutta methods, represented by a free parameter, can we choose the parameter so that the method becomes third order or higher, when computing
a specific quantity, e.g., the square of the solution?