Summer is ideal for running cluster simulation, since no one uses the processors anyway so there is very small queue and no hard drive restrictions. The last simulation I submitted will be the final one if everything goes well... It is the complete 1D problem we have, and it will take 24 hours in 256 processors be completed.
On the theoretical part, there seems to be no way to get an better analytical solution for the envelope of my differential equation. I can get one if I Taylor-expand, but it is not complete since if I add more terms to the expansion I get better answers. Hence since even with Taylor expansion I get approximate (yet closed form) answers, it is likely that I cannot get closed form exact answers.
So I move on to the next step, which is instead of solving the 1D (spatial) problem to introduce time as a second variable. This will give insight into time-dependent effects which we definitely need.
