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I have am using Burgers' Equation with the initial condition of a Gaussian.
The blue curve is the initial function before any time has passed, and the green curve is when the shock first appears. I let more time pass, calculating the shock at each point in time using the equal area rule.
When I plot the shocks that are found on the characteristic plot, I would assume that the shock would first appear where the characteristics first cross. My problem is that it happens at the correct x position, but the time position is wrong (the graph below is an time vs position graph). I have calculated this with a program, but my partner got the same result by hand (note here that I did not do the calculation by hand, and have no idea how he found it).
Why is the times not syncing with the characteristics? Am I just not understanding shocks correctly here?
I ended up solving my problem myself. I had a few issues, but the main one being my time variable was being implemented in a wrong way. The finished product can be found here, write up is included, along with a Windows version of the program so that no python is needed.