Can anyone help me with this error please? '' In an assignment A(I) = B, the number of elements in B and I must be the same. Error in RunFib (line 21) JTime(j) = integral(f​,0,t(1,j),​'Waypoints​',t)./ t(1,j); ''

My code is :

function RunFib

x0=[12 5];

b = 3 ;

tspan = 0 : 0.001 : 10 ;

t0 =tspan(1);

tf=tspan(length(tspan));

A=1/(tf-t0);

[t,x]=ode45(@Fib, tspan , x0 , [] , 3);

        a1 =  ( 15*x(:,1) - 3.*x(:,1).*x(:,2) );
        b1 = ( -5*x(:,2) + 0.5*x(:,1).*x(:,2) );

        f = @(tspan)  ( A.*             (a1.* (a1 .* (15 - 3.*x(:,2)) + b1 .* (0.5 .* x(:,2)) ) + b1 .*  
                         ( a1 .* (-3 .* x(:,1)) + b1 .* (-5 + 0.5.* x(:,1)) )  ).^2  ./ (a1.^2 + b1.^2).^3 );

        t= (0:0.5:10);
        N = length(t);
        JTime = zeros(1,N);
         for j = 1:N
              JTime(j) = integral(f,0,t(1,j),'Waypoints',t)./ t(1,j);
         end  

figure(2)
semilogy(t,JTime,'r+-')

1;

function dx = Fib(t,x,b)

dx=zeros(2,1);

dx0 = 15 * x(1) - b * x(1).* x(2);
dx1 = -5 * x(2) + 0.5 * x(1).* x(2);

end

Answer 1

[Walter Roberson]

Your f takes an input and ignores it and returns something that is size(x,1) elements. The integral of this is probably not going to be a single value.

[Avan Al-Saffar]

In this case, what should I do please?

Note: I used this code for a system of one equation ( dxdt = N0*sin(omega*t)*x*(1-x/K) ) and I got a good results.

[Walter Roberson]

You should ask yourself whether you should really be using integrate(). It looks to me as if you have a specific set of points that you want to calculate the area over, instead of having a function with a variable. If you have a set of points to integrate look at trapz()

[Avan Al-Saffar]

Sorry, may be I could not understand what do you mean exactly but I need to use the results from the function f.

[Walter Roberson]

You are currently doing the equivalent of

f = @(x) [17 9]

which is to say your function f ignores its input and always returns the same thing, a list of values. What are you expecting that the result would be?

Also, you currently have

function dx = Fib(t,x,b)

dx=zeros(2,1);

dx0 = 15 * x(1) - b * x(1).* x(2);
dx1 = -5 * x(2) + 0.5 * x(1).* x(2);

end

That routine computes dx0 and dx1 but then it throws them away and returns the zeros(2,1) from the

dx=zeros(2,1);

You need

function dx = Fib(t,x,b)

dx0 = 15 * x(1) - b * x(1).* x(2);
dx1 = -5 * x(2) + 0.5 * x(1).* x(2);
dx = [dx0; dx1];

end