Are there any books, research on solving a non-linear ordinary differential equation (not a stochastic differential equation) with one normally distributed initial condition?
One simple way would be solving the ODE for a group of initial conditions sampled from the normal distribution.
Another method I found for an arbitrary probability distribution is: https://pubs.aip.org/aip/jcp/article/74/7/3852/217973/Stochastic-sensitivity-analysis-in-chemical
Another method I have seen is using moments but it does not give an exact solution. Are there any methods taking advantage of the normal distribution in particular?
Thank you,
Alex