Time domain solutions do not exist for more than a dozen neurons. At least they did not when I took a computational neuroscience MOOC a couple of years ago. State of the art at the time was the nervous system of an earthworm. That is, if you consider what you actually need to do to simulate how potentials will change in the brain over time give a certain starting state and stimuli, the math gets so complicated (and awkward) so quickly that it's not really tractable with the mathematical (or simulation) apparatus we currently have to go beyond such trivial systems.