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Selected Projects 20<strong>16</strong>-<strong>18</strong><br />
My main job at the beginning was to derive the<br />
order conditions needed to design higher order<br />
multi-derivative methods. I derived the two derivative<br />
Runge-Kutta order conditions up to 6th order<br />
using what is k<strong>no</strong>wn as Butcher trees. Just the one<br />
derivative derivation had 37 trees, after including<br />
the second derivative, it increased tremendously.<br />
Some trees had around 15 sub-derivations; this was<br />
a tedious job that taught me a lot on how to be efficient<br />
and optimal. After deriving all the order conditions,<br />
they had to be included into a code that finds<br />
numerically optimal multi-derivative Runge-Kutta<br />
methods and tests these methods for accuracy and<br />
for the sharpness of the SSP condition on test problems<br />
used previously in the SSP field. We were able<br />
to find methods that gave us sixth order accurate,<br />
and after doing so we found that there are 7th order<br />
methods that work as well. This experience led me to<br />
realize how I want to further my education. Thanks to<br />
a summer grant from the OUR as well as help from<br />
Dr. Gottlieb and Zack Grant, I have decided to pursue<br />
a PhD at UMD in Engineering and Applied Science.<br />
This will be an amazing experience and I very much<br />
look forward to it. To all students out there who have<br />
yet to find the beauty hidden in the intricate curiosity<br />
that some call research, I recommend that you get<br />
involved in research as soon as possible. If you find<br />
that you don’t like it, it is easy to get out; but, if you<br />
find it luring and attractive, you will feel like you have<br />
lost time <strong>no</strong>t doing it earlier. Research is <strong>no</strong>t boring,<br />
as many students might think. It is challenging<br />
and never definitive or mo<strong>no</strong>to<strong>no</strong>us. You’re always<br />
learning something new. Even if you try it once and<br />
don’t like it, you could still try it again, because there<br />
are so many topics unexplored that you are bound to<br />
find something you find interesting.<br />
I’d like to leave you with this quote by the American<br />
biochemist and peace activist, Linus Carl Pauling:<br />
“Satisfaction of one’s curiosity is one of the greatest<br />
sources of happiness in life.”<br />
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