The ODE solver solves first-order ODE problems with the least step count. The program was written in Matlab. The program requires a function, an interval, and an error tolerance. The program meets the most error tolerance requirement (10^-3,...,10^-12).

The project went well. I teamed up with a classmate for this assignment. I created a Google Doc to generate different ideas we could attempt. Then we tried Runge-Kutta (RK), linear multistep, and other methods. We found that most methods couldn't get less than the error tolerance. We try to experiment by combining two RK, and we found out it takes more steps. So we decide to use only one RK method. We found that RK Cash-Karp is the best choice out of all the methods. Then we decided to use it for our project. We have to change the safety factor depending on the error tolerance. We add a way to use the previous value. When the method calculates the y value, it stores the value. If the value is fit the error tolerance, the program will use it.

Code

The GPS program is a simple GPS model. The program is written in C++, and it solves a non-linear system. It has two programs: satellite and receiver. The satellite uses information from the vehicle program and a text file named data.dat about the number of satellites and the vehicle's position. Then the receiver used the satellite's outputs to convert it back into position data.

The project didn't go well. I teamed up with two other classmates. I have experience in computer science, and one of my group members took some computer science. So I decided to work on the satellite myself, and they worked on the receiver. My program's output wasn't accurate. I asked my group about their process on the receiver. They gave me a very vague answer. Then I found out they didn't work on the project at all. There was only a week left until the assignment was due. Since the project was an optional group project, I decided to work myself. In the end, I couldn't get it done. I had too many bugs in the receiver and satellite.