Hello everybody.
In the attached code, when I compute q_1 by NIntegrate is equal to 0.000195151 while the true value for q_1 is 0.0001943732. Of course \Sigma(T) is computed correctly.
What is the reason for this slight difference?
In fact, I tried to write the below formula
like this:
Is it true?
What’s the problem?
At last, I should say that I must use NIntegrate in my computation.
Untitled-5.nb (18.2 KB)
Your integrals have a closed symbolic form, and it seems that the value given by NIntegrate is correct:
In[1742]:=
Integrate[f0[s] Vbar[s]*f0[u] Vbar[u], {s, 0, T}, {u, 0, s}] + \[Rho]*
Integrate[
Vbar[s]*Subscript[\[Lambda], 2][s, u] Vbar[u], {s, 0, T}, {u, 0, s}]
% // N
Out[1742]= (-287 + 3588 E^2 + 7943 E^4)^2/(131072000000 E^8) - (
3 (-962033 + 7920336 E^2 + 1970629 E^4))/(26214400000 E^4)
Out[1743]= 0.000195151
Yes, It seems correct.
I really appreciate it. Thank you Gianluca for your great help and time in recent days.
I don’t know what to say!
That’s very kind.
I am glad you appreciated my help!