I am looking for actual applications where differential equations are solved using implicit methods that boil down to solving a tridiagonal every time step. I found that there are heat equations and others that boil down to tridiagonals, but I couldn't find any real world applications and values used.
I also read the answer in This post, which mentioned looking at Princeton companion to mathematics to find applications, but what I need the actual values used one of these applications when an experiment is done.
I need this to test the accuracy of my implementation to solve this. If there is a easier way to test the accuracy of a solver, I am open to those ideas as well.