Q: Plotting solution of ParametricNDSolve not possible for needed parameter range I wish to numerically solve a parametric decay model. The system of equations is fairly simple. But plotting the solution for a wider parameter range is not possible (see code). 
Mathematica throws 2 error messages:


*

*ParametricNDSolve::nderr: Error test failure at t == 0.`; unable to continue.

*InterpolatingFunction::dmval: Input value {2.04286*10^-11} lies outside the range of data in the interpolating function. Extrapolation will be used.


I tried to play around with the accuracy goal because of the small parameters (especialle k3), but somehow a smaller accuracy goal seems to work better (but not good enough) which to me is very strange...
Any ideas?
Here is my compilable code:
ClearAll[k1, k2, k3];

tmin = 0;
tmax = 1000*10^-9;

k1try = 1*10^5;
k2try = 1*10^-10;
k3try = 1*10^-28;

c = 6.2*10^16;

fitmodel = ParametricNDSolve[
  {n'[t] == -k1*n[t] - k2*n[t]^2 - k3*n[t]^3,
   PL[t] == (n[t]^2 )/(c^2),
   n[0] == c,
   PL[0] == 1},
  PL, {t, tmin, tmax}, {k1, k2, k3}, AccuracyGoal -> 40]


Plot[Evaluate[
  Table[PL[k1try, k2try, k3][t] /. fitmodel, {k3, 1*10^-28, 10*10^-26,
     10*10^-28}]], {t, tmin, tmax}, PlotRange -> All]


A: tmin = 0;
tmax = 10^(-6);

k1try = 1*10^5;
k2try = 1*10^-10;
k3try = 1*10^-28;
c = 6.2*10^16;

fitmodel = 
 ParametricNDSolve[{n'[t] == -k1*n[t] - k2*c*n[t]^2 - k3*c*c*n[t]^3, 
   n[0] == 1}, n, {t, tmin, tmax}, {k1, k2, k3}]


Plot[Evaluate[
  Table[n[k1try, k2try, k3][t]^2 /. fitmodel, {k3, 1*10^-28, 
    10*10^-26, 10*10^-28}]], {t, tmin, tmax}, PlotRange -> All]


