Unable to meet integration tolerances without reducing the step size below the smallest value allowed

Hi.

I have a problem with drawing a plot. Please guide me.

My program is as follows:

main:

tspan = [0 5e-9];                  
y0 = [0.2,0.2,0.2];     
[t,y] = ode45(@rate_fano,Time,y0);
size(t);
t=t*1e9;        
y = abs(y);                                        


params              % input of needed parameters       

 
figure(1) 
plot(t, y(:,1));   % divided to normalize
xlabel('time [ns]','FontSize',14);  % size of x label
ylabel('Arbitrary units','FontSize',14);    % size of y label
set(gca,'FontSize',14);                 % size of tick marks on both axis
legend('N', 'Location','SE')  % legend inside the plot);   % divided to normalize
figure(2) 
plot(t, y(:,2));   % divided to normalize
xlabel('time [ns]','FontSize',14);  % size of x label
ylabel('Arbitrary units','FontSize',14);    % size of y label
set(gca,'FontSize',14);                 % size of tick marks on both axis
legend('A+', 'Location','SE')  % legend inside the plot);   % divided to normalize

function:

% N == y(1)
%A+ == Y(2)
%A- == Y(3)
function yx = rate_fano(t,y)

 params              % input of needed parameters 
 
 r_R=(-p*gamma_c)/(1i*(deltac)+gamma_T);
 
    U=(2.*epsilon0.*ref_index.*ref_indexg)./(hbar_ev.*w_s);
    B=(1+(abs(r_R))).*(1-(abs(r_R)));
    D=(conf.*(g_n)-henry_i);
    sigmaa=U.*((B./D));
    
    
 yx(1)=I./(e.*V_a)-y(1)./tau1-(V_g.*g_n.*(y(1)-N_0).*sigmaa.*(abs(y(2)))^2)./V_m; 
 yx(2)=1/2*(1-1i*henry).*conf.*V_g.*g_n.*(y(1)-N_ss).*y(2)+gamma_L.*((y(3)./r_R-y(2)));
 yx(3)=(-1i.*deltaw-gamma_T).*y(3)-p.*gamma_c.*y(2);
 
 yx= yx';

parameters:

c = 2.99792458e8;                   
e = 1.6021766208e-19;         
h = 6.626068e-34;                                                            
h_eV = h/e; 
hbar = h/(2*pi);           
hbar_ev = hbar/e;
epsilon0 = 8.854187817e-12;        

p=-1;


L = 5e-6;                 
A = 0.21e-12;

conf = 0.5;           
conf_NC =0.3;          

V_a=A*L;                  
V_m = V_a/conf;           
V_NC=0.24e-18;


ref_index = 3.5;      
ref_indexg=3.5;       
V_g = c/ref_index;     
tau1 = 0.5e-9;                   
g_n = 5e-21;             
N_0=1e24;   
N_ss=1e24;

I =0.5e-3;              

   
henry_i=10;         
henry = 1;                


Qt = 500;
Qi = 14300;
Qp = 10000;

lambda0 = 1554e-9;
deltalambda = 0.01e-9;
lambda_start = 1540e-9;
lambda_end = 1560e-9;
lambda = lambda_start:deltalambda:lambda_end;
omega = 2*pi*c./lambda;
omega0 = omega(find(lambda==lambda0));

gamma_i = omega0/(2*Qi);
gamma_p = omega0/(2*Qp);
gamma_T = omega0/(2*Qt);
gamma_c = gamma_T-gamma_i-gamma_p;
gamma_L=V_g/(2*L);


w_r=1.2121*10^15;
w_s=1.2121*10^15;
w_c=1.2125*10^15;

                
rho=(2*epsilon0*ref_index*c)./gamma_c.*hbar_ev.*w_r; 
r_L=1;                            
deltaw=0*gamma_T;
deltac=1.2125*10^15-1.2121*10^15;

[Star Strider]

The error in the title of your Question indicates that ode45 encountered a singularity (±Inf), and stopped because of that. You first need to check your code to be certain there are no errors, including parameter magnitudes. If there are none, then it is simply not possible to integrate your function over the complete time span you want.

[mohammad heydari]

thank you.