The help of Mathematica doesn't say so much about the
NDSolve, and I never considered much about it even after I met the warning message
for several times when I was trying to solve a set of PDEs these days: every time I met it I would simply considered it as a proof for the defect of my assumption for the initial or boundary condition, and my resolution strategy for it is to modify the conditions or sometimes I will also lower the value of the
PrecisionGoal as the help says.
However, this time I can't ignore it anymore, for I accidentally found that for one of my assumptions, the suitable
PrecisionGoal for it is a negative integer…
The thing named "Precision" in my mind was always a positive integer, but this time it is negative! Why?…… What's the exact effect of "PrecisionGoal" option for