The difference between first and second order solution

Stochastic simulations
1

Dear all

I have problem with quodratic tern in one equation of my mod file. The equation is as follows:
mud=Omega*((1-taustar)R( 1-tau_adj*( (Dstar-steady_state(Dstar))^2)/ (1-tauB) )-ebar(+1)/ebarRstar);
tau_adj is a parameter, and Dstar is
I found that when I set the solution order equals 1, there is no difference when I introduce the quadratic term:
tau_adj( (Dstar-steady_state(Dstar))^2)
But when I set the solution order equals 2, the introduced quadratic term has an effect, i.e. , the result with tau_adj>0 is different with that of tau_adj=0.
Where is the problem?
Thank you.

2

I am not sure I understand the problem. You are introducing a term whose first order derivative evaluated at the steady state
2 \tau (\bar D^*-\bar D^*)
is 0. The second derivative in contrast is
2 \tau \neq 0
Thus, it introduces a difference at second order.

3

Yes, I know this difference, but I mean, when order=1, the dynamics of the model has no difference between tau_adj=0 and tau_adj>0.

4

As I said, the first order derivative evaluated at the steady state is 0. If something is 0 at first order, it cannot play a role at first order.