How can I overcome from this problem? any another method to solve this.

ti = 0;
tf = 70E-6;
tspan=[ti tf];

y0= [(1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (1e-2)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      ((-3.14).*rand(70,1) + (3.14).*rand(70,1))
      ];



N = 70;

yita_mn = [
circshift(diag(ones(1,N)),1) + circshift(diag(ones(1,N)),-1)
].*(0.01);
tp = 1E-9;
o = sort(10e2*rand(1,N),'ascend');
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N,o),tspan./tp,y0);

Warning: Failure at t=4.285732e+02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (9.094947e-13) at time t.

r = (1/70).*( exp(i.*Y(:,3)) + exp(i.*Y(:,6)) + exp(i.*Y(:,9)) + exp(i.*Y(:,12)) + exp(i.*Y(:,15)) ...
    +exp(i.*Y(:,18)) +exp(i.*Y(:,21)) +exp(i.*Y(:,24)) + exp(i.*Y(:,27)) + exp(i.*Y(:,30)) + exp(i.*Y(:,33)) ...
    + exp(i.*Y(:,36)) + exp(i.*Y(:,39)) +exp(i.*Y(:,42)) + exp(i.*Y(:,45)) + exp(i.*Y(:,48)) + exp(i.*Y(:,51)) ...
    + exp(i.*Y(:,54))+ exp(i.*Y(:,57)) + exp(i.*Y(:,60)) + exp(i.*Y(:,63)) + exp(i.*Y(:,66)) + exp(i.*Y(:,69)) ...
    + exp(i.*Y(:,72)) + exp(i.*Y(:,75)) + exp(i.*Y(:,78)) + exp(i.*Y(:,81)) + exp(i.*Y(:,84)) + exp(i.*Y(:,87)) ...
    + exp(i.*Y(:,90)) + exp(i.*Y(:,93)) + exp(i.*Y(:,96)) + exp(i.*Y(:,99)) + exp(i.*Y(:,102)) + exp(i.*Y(:,105))...
    + exp(i.*Y(:,108)) + exp(i.*Y(:,111)) + exp(i.*Y(:,114))+ exp(i.*Y(:,117)) + exp(i.*Y(:,120)) + exp(i.*Y(:,123))...
    + exp(i.*Y(:,126)) + exp(i.*Y(:,129)) + exp(i.*Y(:,132)) + exp(i.*Y(:,135)) + exp(i.*Y(:,138)) + exp(i.*Y(:,141))...
    + exp(i.*Y(:,144)) + exp(i.*Y(:,147)) + exp(i.*Y(:,150)) + exp(i.*Y(:,153)) + exp(i.*Y(:,156)) + exp(i.*Y(:,159)) ...
    + exp(i.*Y(:,162)) + exp(i.*Y(:,165)) + exp(i.*Y(:,168)) + exp(i.*Y(:,171)) + exp(i.*Y(:,174)) + exp(i.*Y(:,177)) ...
    + exp(i.*Y(:,180)) + exp(i.*Y(:,183))+ exp(i.*Y(:,186)) + exp(i.*Y(:,189)) + exp(i.*Y(:,192)) + exp(i.*Y(:,195)) ...
    + exp(i.*Y(:,198)) + exp(i.*Y(:,201))+ exp(i.*Y(:,204)) + exp(i.*Y(:,207)) + exp(i.*Y(:,210)));


M = max(abs(r));

plot(T,M)

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

dy = zeros(4*N,1);
dGdt = zeros(N,1);
dAdt = zeros(N,1);
dOdt = zeros(N,1);
P = 0.50;
a = 0;
k = 0.01;
T = 2000;
tp = 1E-9;
Gt = y(1:3:3*N-2);
At = y(2:3:3*N-1);
Ot = y(3:3:3*N-0);
for i = 1:N
    dGdt(i) = (P - Gt(i) - (1 + 2.*Gt(i)).*(((At(i)))^2))./T ; 
    dAdt(i) = (Gt(i)).*(At(i));
    dOdt(i) =(-a).*Gt(i) + o(1,i).*tp;  
    for j = 1:N
        dAdt(i) = dAdt(i) + yita_mn(i,j)*(At(j))*cos(Ot(j)-Ot(i));
        dOdt(i) = dOdt(i) + yita_mn(i,j)*((At(j)/At(i)))*sin(Ot(j)-Ot(i));
    end
end
dy(1:3:3*N-2) = dGdt;
dy(2:3:3*N-1) = dAdt;
dy(3:3:3*N-0) = dOdt;

n1 = (1:70)';
n2 = circshift(n1,-1);
n211 = n1 +180;
n212 = circshift(n211,-1);
n230 = circshift(n211,1);

j2 =  3*(1:70)-1;
j5 = circshift(j2,-1);
j8 = circshift(j2,-2);
j209 = circshift(j2,1);

dy(n211) = (o(1,n2).' - o(1,n1).').*tp - a.*(Gt(n2) - Gt(n1)) - (k).*(y(j2)./y(j5)).*sin(y(n211)) - (k).*(y( j5)./y(j2)).*sin(y(n211)) + (k).*(y(j8)./y(j5)).*sin(y(n212)) + (k).*(y(j209)./y(j2)).*sin(y(n230));  

end

Answer 1

[Torsten]

As long as you don't know the reason for the integration problem, you won't be able to overcome it.

We can only refer to the different general strategies to overcome this error message:

Try a different integrator.

Try changing RelTol and AbsTol of the integrator.

Check your model for errors.

Check your code for errors.

[John D'Errico]

And...

Don't use 3.14 as pi. That is not pi. Pi is already defined in MATLAB anyway.

format long g
pi

ans = 
          3.14159265358979