05/25/2022, 04:04 AM
Alright!
For fucks sakes. I got by by the skin of my teeth. I have an analytic solution. It's going to be a while to get it coherent and make a write up well enough. I got super fucking lucky though. The infinite composition needed to solve this first order difference equation converges like:
\[
\sum \frac{1}{n\log(n)^2}\\
\]
Which, is like the slowest possible convergence. So don't expect an efficient algorithm as of yet. But I can derive an analytic solution because thank the fuck that it wasn't \(\frac{1}{n\log(n)}\) which diverges.
So the solution I can construct analytically converges, but it's as slow as fucking possible -_-.
For fucks sakes. I got by by the skin of my teeth. I have an analytic solution. It's going to be a while to get it coherent and make a write up well enough. I got super fucking lucky though. The infinite composition needed to solve this first order difference equation converges like:
\[
\sum \frac{1}{n\log(n)^2}\\
\]
Which, is like the slowest possible convergence. So don't expect an efficient algorithm as of yet. But I can derive an analytic solution because thank the fuck that it wasn't \(\frac{1}{n\log(n)}\) which diverges.
So the solution I can construct analytically converges, but it's as slow as fucking possible -_-.