I wrote a program to simulate the string equation.

One thing that surprised me was that at first there was no difference between the small angle and large angle models.  Then I realized why.  I had set k = delta = L = rho = 1.

If a string is stretched so delta = L, the small angle equation is exact even for large angles.

This is not exactly a practical theorem.  Delta = L implies the original length was zero, so the string is stretched to infinite times its original length.

I may try to do another simulation that does show the difference between the two models, but the large angle model seems like it can have problems with numerical stability.

(Note: When I look at the program’s source code now, it seems I deleted the initial condition the comments talk about)