I am trying to numerically find an equilibrium (maximum) of a function using its differential. The following is a simplified version.
myEquilibrium[.5] // 0.5 which is correct
The function should be constrained to positive s, which is why I included the
s[t]<10^-4 requirement. However this does not seem to work.
myEquilibrium[-.5] // -0.5 but should be 10^-4
The NDSolve should also not go to
0 exactly, as the real, non-simplified version contains a
1/s[t] in the differential. That's another reason I want the procedure to stop at
myEquilibrium // 0. but should be 10^-4
Finally, I often get
NDSolve::mxst: Maximum number of 10000 steps reached at the point t == 6.57563031118913721074693815431*^4952. >> and
NDSolve::ndsz: At t == 1.79769313486*^308, step size is effectively zero; singularity or stiff system suspected. >>. What would typically solve this issue?