why I'm getting an error of index exceeds the number of element? how to fix it?

ti = 0;
tf = 2.50E-9;
tspan=[ti tf];
y0=[0; 0; 0];
yita_mn = 0.01;
N = 5;
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan,y0);

Index exceeds the number of array elements. Index must not exceed 3.

Error in solution>rate_eq (line 32)
Nt = y(1:3:3*N-2);

Error in solution (line 7)
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan,y0);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

subplot 211
plot(T,Y(:,2));

subplot 212
plot(T,Y(:,3));



function dy = rate_eq(t,y,yita_mn,N)

dy = zeros(3*N,1);
dNdt = zeros(N,1);
dSdt = zeros(N,1);
dWdt = zeros(N,1);

P =0.1;
a =0.1;
tc = 230E-6;
tp =5.4E-9;
o = 2E5;
k_c = 1/tp;

Nt = y(1:3:3*N-2);
St = y(2:3:3*N-1);
Wt = y(3:3:3*N-0);

for i = 1:N
    dNdt(i) = (P - Nt(i).*((abs(St(i)))^2 +1))./tc ; 
    dSdt(i) = (Nt(i)-a).*((St(i))./tp);
    dWdt(i) = o;  
    for j = 1:N
        dSdt(i) = dSdt(i)+yita_mn(i,j)*k_c*(St(j))*cos(Wt(j)-Wt(i));
        dWdt(i) = dWdt(i)+yita_mn(i,j)*k_c*((St(j)/St(i)))*sin(Wt(j)-Wt(i));
    end
end

dy(1:3:3*N-2) = dNdt;
dy(2:3:3*N-1) = dSdt;
dy(3:3:3*N-0) = dWdt;

Loop_in = Loop_in+1;
Loop = Loop_in;
CalLoop=sprintf('Calculation Loop',Loop);
disp(CalLoop);
end

===============================================

Index exceeds the number of array elements. Index must not exceed 3.

Error in untitled2>rate_eq (line 31)

Nt = y(1:3:3*N-2);

Error in untitled2 (line 7)

[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan,y0);

Error in odearguments (line 92)

f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

=======================================================

[Torsten]

y0 has three elements:

y0=[0; 0; 0];

so N in your code must be 1, not 5.

[SAHIL SAHOO]

ti = 0;
tf = 2.50E-9;
tspan=[ti tf];
y0=[0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0];
yita_mn = 0.01;
N = 5;
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan,y0);

Index in position 2 exceeds array bounds. Index must not exceed 1.

Error in solution>rate_eq (line 41)
dSdt(i) = dSdt(i)+yita_mn(i,j)*k_c*(St(j))*cos(Wt(j)-Wt(i));

Error in solution (line 7)
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan,y0);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

subplot 211
plot(T,Y(:,2));

subplot 212
plot(T,Y(:,3));



function dy = rate_eq(t,y,yita_mn,N)

dy = zeros(3*N,1);
dNdt = zeros(N,1);
dSdt = zeros(N,1);
dWdt = zeros(N,1);

P =0.1;
a =0.1;
tc = 230E-6;
tp =5.4E-9;
o = 2E5;
k_c = 1/tp;

Nt = y(1:3:3*N-2);
St = y(2:3:3*N-1);
Wt = y(3:3:3*N-0);

for i = 1:N
    dNdt(i) = (P - Nt(i).*((abs(St(i)))^2 +1))./tc ; 
    dSdt(i) = (Nt(i)-a).*((St(i))./tp);
    dWdt(i) = o;  
    for j = 1:N
        dSdt(i) = dSdt(i)+yita_mn(i,j)*k_c*(St(j))*cos(Wt(j)-Wt(i));
        dWdt(i) = dWdt(i)+yita_mn(i,j)*k_c*((St(j)/St(i)))*sin(Wt(j)-Wt(i));
    end
end

dy(1:3:3*N-2) = dNdt;
dy(2:3:3*N-1) = dSdt;
dy(3:3:3*N-0) = dWdt;
end

why still this is not working,?

[Torsten]

Because yita_mn must be of size (5x5), not of size (1x1).

[Karim]

because you are trying to acces

yita_mn(i,j)

as if it is a matrix, however you initalize

yita_mn = 0.01;

as a scalar, hance an error is thrown the moment either i or j are greater then 1.

Looking at the code you will need to make sure yita_mn has N rows and N columns. Or remove the indexing (i,j) in the routine to just use the scalar.

[SAHIL SAHOO]

ti = 0;
tf = 1E-8;
tspan=[ti tf];
y0=[1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1]*10E-8;
yita_mn = [0 1 0 0 1; 1 0 1 0 0; 0 1 0 1 0; 0 0 1 0 1; 1 0 0 1 0]*(0.001);
N = 5;
tp = 5.4E-9;
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N),tspan./tp,y0);


subplot 211
plot(T,Y(:,2));

subplot 212
plot(T,Y(:,3));




function dy = rate_eq(t,y,yita_mn,N)

dy = zeros(3*N,1);
dNdt = zeros(N,1);
dSdt = zeros(N,1);
dWdt = zeros(N,1);

P = 14.5;
a = 0.1;
tc = 230E-6;
tp =5.4E-9;
o = 2E3;
k_c = 1/tp;

Nt = y(1:3:3*N-2);
St = y(2:3:3*N-1);
Wt = y(3:3:3*N-0);

for i = 1:N
    dNdt(i) = (P - Nt(i).*((abs(St(i)))^2 +1))./tc ; 
    dSdt(i) = (Nt(i)-a).*((St(i))./tp);
    dWdt(i) = o;  
    for j = 1:N
        dSdt(i) = dSdt(i)+yita_mn(i,j)*k_c*(St(j))*cos(Wt(j)-Wt(i));
        dWdt(i) = dWdt(i)+yita_mn(i,j)*k_c*((St(j)/St(i)))*sin(Wt(j)-Wt(i));
    end
end

dy(1:3:3*N-2) = dNdt;
dy(2:3:3*N-1) = dSdt;
dy(3:3:3*N-0) = dWdt;
end

I dont know, why still this its not working?