I have eqs about the `NDSolve`

, I know this code given the solving automatically.

How can I find out what method is used behind the scenes? How can I gauge the reliability level, find how many iterations have been used, the order of method. How can I estimate the error?

I found hints on this site, but I still do not fully understand.

It is impossible to say `NDSolve`

has automatically solution for publishing paper?

I used this code related to my system:

`r = 0.431201; β = 2.99 *10^-6; σ = 0.7; δ = 0.57; {m = 0.3, η = 0.1, μ = 0.1, ρ = 0.3}; S = {N1'[t] == r N1[t] (1 - β N1[t]) - η N1[t] I1[t], I1'[t] == σ + (ρ N1[t] I1[t])/( m + N1[t]) - δ I1[t] - μ N1[t] I1[t]}; c = {N1[0] == 1, I1[0] == 1.22}; Select[Flatten[ Trace[ NDSolve[{S, c}, {N1, I1}, {t, 0, 30}], TraceInternal -> True]], !FreeQ[#, Method | NDSolve`MethodData] &] `

but I don’t understand the output.