how to store the value of intersection points from fzero into a vector

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I am calculating fzero using fzero function. For each value of 'a' (ranging from 0.1 to 1) I need to get value of u*(intersection of fun1 and fun2) as shown in below graph(just for reference). And then i want to store the value of u* in a different vector. Can someone please help me to get the values and store them.Below is my current code which is calculating u* only for a=0.4.
function y = difference(u,d1,n,a,m,T,PsByN_0,UmaxN_0)
d1=20;
n=10^-11.4;
ne=0.5;
m=2.7;
a=0.4;
T=1;
PsByN_0dB=5;
PsByN_0=10.^(PsByN_0dB/10);
UmaxdB = 5;
UmaxN_0=10.^(UmaxdB/10);
u=0.01:0.001:2;
fun1 = @(u) (-1./u).*log(((d1^m)./(a*ne*PsByN_0*T*u+d1^m)*a)./(1-a));
fun2 = @(u) (1./u).*log(((-exp(u.*UmaxN_0).*(exp(-PsByN_0.*u)))./(u.*UmaxN_0+PsByN_0.*u)).*(PsByN_0.*u)-(PsByN_0.*u.*(exp(-PsByN_0.*u))).*(expint(u.*UmaxN_0+PsByN_0.*u))+(exp(-PsByN_0.*u))+((PsByN_0.*u).*(exp(-PsByN_0.*u))).*(expint(PsByN_0.*u))+(exp(u.*UmaxN_0))./((UmaxN_0/PsByN_0)+1));
fun = @(u) (fun1(u) - fun2(u));
%g0=fzero(fun,[0.001,0.02])
g0 = fzero(fun,[0.01])
fun1(g0)
fun2(g0)
plot(u,fun1(u));
hold on;
grid on;
plot(u,fun2(u));
hold on;
grid on;

Accepted Answer

Torsten
Torsten on 7 Aug 2022
Edited: Torsten on 7 Aug 2022
Before using fzero or fsolve, you should check whether fun1 - fun2 really has a zero.
To do this, uncomment the lines
u=[0.01:0.01:2];
plot(u,fun(u,a(3)))
and insert the a-value (in this case a(3)) for which you want to perform the test.
For a>0.5, it seems that fsolve has problems to find a solution. Check it with the method I suggested.
d1=20;
n=10^-11.4;
ne=0.5;
m=2.7;
a=0.01:0.01:0.5;
T=1;
PsByN_0dB=5;
PsByN_0=10.^(PsByN_0dB/10);
UmaxdB = 5;
UmaxN_0=10.^(UmaxdB/10);
fun1 = @(u,a) (-1./u).*log(((d1.^m)./(a.*ne.*PsByN_0.*T.*u+d1.^m).*a)./(1-a));
fun2 = @(u) (1./u).*log(((-exp(u.*UmaxN_0).*(exp(-PsByN_0.*u)))./(u.*UmaxN_0+PsByN_0.*u)).*(PsByN_0.*u)-(PsByN_0.*u.*(exp(-PsByN_0.*u))).*(expint(u.*UmaxN_0+PsByN_0.*u))+(exp(-PsByN_0.*u))+((PsByN_0.*u).*(exp(-PsByN_0.*u))).*(expint(PsByN_0.*u))+(exp(u.*UmaxN_0))./((UmaxN_0/PsByN_0)+1));
fun = @(u,a) (fun1(u,a) - fun2(u));
%u=[0.01:0.01:2];
%plot(u,fun(u,a(3)))
%g0=fzero(fun,[0.001,0.02])
options = optimset('Display','none');
g0 = arrayfun(@(a)fsolve(@(u)fun(u,a),[0.01],options),a)
g0 = 1×50
1.6739 1.4530 1.3231 1.2304 1.1581 1.0986 1.0480 1.0039 0.9646 0.9293 0.8971 0.8674 0.8399 0.8141 0.7900 0.7671 0.7455 0.7248 0.7050 0.6861 0.6678 0.6501 0.6330 0.6164 0.6001 0.5843 0.5688 0.5536 0.5386 0.5238
%fun(g0,a)
plot(a,g0)
  5 Comments
Torsten
Torsten on 7 Aug 2022
@Dhawal Beohar comment moved here
Thanks for explaining things. I really appreciate your help. Thank you so much for being there !!!

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