To be specific, a linear solver can be (as in I have done) written in a week.

A serious non-linear solver that handles legacy Spice models is another beast entirely. And if you want to integrate modern advances in algebraic-differential systems you take that to a higher level.

These are not partial differential equations such as you find in Navier-Stokes. These are sparse non-linear differential equations that do not parallelize nearly as simply.

Another example of related problems that parallelize poorly even though they are linear are the FDTD formulations for Maxwell's equations. These are relatively simple systems, but the bottleneck is almost always the memory bandwidth because it is so hard to parallelize.