Bisection method + Differential equation question

I need to calculated 100 values using differential equation and bisection method, but it is giving me only 1 value. I have 100 a1 and a2 values initially, and the time needed when m>1 should be calculated. this is where I got stuck..

tmax=10;
tmin=0;
error=tmax-tmin;

for i=1:100
    dmdt=@(t,m)[-m(1).*a1(i);m(1).*a1(i)-m(2).*a2(i)];
    while error>10^-5
        treal=(tmax+tmin)/2;
        [t,m]=ode45(dmdt,[0 treal(i)],[1;0]);
        if m(end,2)>1
            tmax=treal(i);
        else tmin=treal(i);
        end
        error=tmax-tmin;
    end
end

treal

I have it as treal and it is giving me only 1 value instead of 100.

Answer 1

[Geoff Hayes]

Are you not observing some sort of Index exceeds matrix dimensions error? Look at the following lines from your while loop

 while error>10^-5
     treal=(tmax+tmin)/2;
     [t,m]=ode45(dmdt,[0 treal(i)],[1;0]);
     % etc.
 end

On each iteration of the while loop, treal is set to a scalar value (since tmax and tmin are scalar values). The following line tries to access treal(i) which, for i>1 should throw the above error message.

It may be that you want to do the following instead

 while error>10^-5
     treal(i)=(tmax+tmin)/2;
     [t,m]=ode45(dmdt,[0 treal(i)],[1;0]);
     % etc.
 end

so that as long as we are in the while loop for the ith iteration of the for loop, we continue to update treal.

I suggest replacing i with k (as your index value) since i (and j) is also used as the representation of the imaginary number.