Computational Project #2 - Group 5
This computational group project involves implementing numerical methods for ordinary
differential equations (ODEs) in two directions. In the first direction, we must solve either 2D or
3D ordinary differential equations using an explicit and an implicit method.
Group 5 maintained the same assigned roles as Computational Project #1. Thus, follows
with Team Leader - Will Mahnke, Project Designer - Tim Guan, Programmer - Tiffany Liu,
Reporter - Natalya Rodriguez, and Documenter - Chris Pang. Moreover, extra work and
assistance by other group members included Chris helping Tiffany with the programming portion
and Tim helping Natalya write portions and proofread this report. And Will being responsible for
the overall quality control of the entire project.
Meeting #1 - December 3rd, 2023
On December 3rd, Group 5 discussed scheduling group meetings. Each member shared
their availability for the upcoming week in hopes of permitting a meeting to start the project with
basic ideas, information, and thoughts to share. However, Natalya was out of town for the
weekend. To supplement her absence and for the sake of convenience, she proposed meeting
through Zoom, which worked well with the rest of the group. Overall, Group 5 struggled with
the same hurdles as with Computation Project #1— which was time management and meeting
times. The group felt stressed due to our upcoming finals because it was near the end of the
quarter. Moreover, scheduling was difficult as most members had other obligations or unforeseen
circumstances. However, our group still came together via Zoom to meet for 1 hour.
Throughout the meeting, Will, Chris, and Natalya discussed what methods to use and
concluded by using the Adam-Bashforth and Adam-Moulton methods. Although Tim did not
attend the meeting, he gave the members his thoughts and ideas. This included referring back to
Professor Park’s lecture notes along with providing a reference to spearhead the project in the
right direction using “Example 6.25” (Pg. 349) in the textbook Numerical Analysis 3rd Edition
(2017) by, Timothy Sauer, regarding the Backward Euler Method, which was valuable to our
meeting since Chris, Will, and Natalya referenced this as a critical point.
In the meeting, there was a lot of discussion on how to make our project good. Because
of time constraints and complexities in upholding the standard of numerical analysis, our group
discussed what platforms would be most convenient to utilize, including Google Colab, Jupyter
Notebook, and other available online compilers. Ultimately, our group decided that using Google
Colab would be the best since we knew the platform's streamlined and user-friendly nature.
Moreover, since we had already presented our first computational project in class, we had more
space to divide the work within the group. We decided that Chris would help Tiffany with the
programming portion and Tim would help Natalya write the report, with Will also assisting with
both.
Programming Portion:
Regarding our code, we used the explicit form of Adam-Bashforth and the implicit form
of Adam-Moulton. Chris and Tifanny programmed the given equations (see above) into Google
Colab’s Python compiler to solve the ODEs in the problem. In contrast with CP1’s programming
portion, which had a few difficulties due to miscommunication and misinterpretation, Chris and
Tiffany worked cohesively and diligently to uphold good programming practices. When graphing
our solutions, both methods came close to the exact ODE solution such that everything worked
properly. (Our graphs below compare the sanity check and actual solution ODE.)
Final Thoughts:
Our advice to future groups for CP2 is to organize the group fast, with communication
and cohesion imperative to success. Moreover, having everyone well-versed in both numerical
methods will expedite the process more quickly regarding the work involved— given our limited
time and urgency toward completing the project near the end of the quarter. Moreover, as
Reporters, we observed good group programming practice and communication skills. Everyone
did strictly as assigned and helped each other out as much as they could.