Um, so you have a decent sized problem. It takes a long time to solve. No surprise. That you want it to be faster is only a reflection of the fact that we expect everything to happen immediately.
What it looks like to me is that you got fsolve to work on one problem, so then you decided to apply it to thousands of problems. Suddenly, fsolve is not fast enough.
There are several ways to improve the time.
1. Get a faster computer.
2. Use the profile tool to see if your code can be improved. Again, no surprise that sometimes people write code that is less than optimal.
3. Reduce the size of your problem.
4. Apply a tool the parallel toolbox to solve the many problems at once. Of course, this requires a (not cheap) toolbox, and that you learn to use it effectively, AND that you have sufficient cores to gain throughput.
5. Apply a GPU based tool to enhance the speed of some bottleneck point in your code. Again, this requires various things to be true.
There is no magic to be done to fsolve that will suddenly make it run faster. If there were, then it would be the default setting. The problem is not with fsolve here, but with your expectations or with your code.
