Iteration error iter=0

Hello,

I am trying to solve a 2nd order difference equation with given bounds. Specifically:

I need to solve for a sequence of ( for t = 1,2,...,50) such that:

$X_{t+2} = f( X_{t+1}, X_t) $, the exact function is inside the below loop.

Here is my code to solve this system, using shooting method. And it is very strange that I got a sequence of X are all equal for 0 for all t. And more strange, the number of iterations executed (which is denoted iter in the loop are 0).

I have been checking for hours, but could not find the mistake. If any one see what is wrong with my code, plz kindly let me know.

Thanks so much,

        

T = 5;
X = zeros(T+1,1)
X(1) = 10;
iter=0

while (abs(X(T+1)) > TOL);
    X(2) = (LEFT + RIGHT)/2;
    for i = 1:T-1;
        X(i+2,1) = A * (1 + ALPHA * BETA)* (X(i+1,1))^ALPHA + (1-DELTA) * (1 + BETA) * X(i+1,1)...
            - BETA * (A * (X(i,1))^ALPHA + (1 - DELTA) * X(i,1)) * (A * ALPHA * X(i+1,1)^(ALPHA - 1) + (1 - DELTA));
    end;
    if X(T+1,1)< 0
       LEFT = X(2,1);
    elseif X(T+1,1) > 0
       RIGHT = X(2,1);
    else break;
    end;
    iter=iter+1
end;

Answer 1

[Geoff Hayes]

heidi - try using the MATLAB debugger to step through your code to determine what is going on. Note the following code

T = 5;
X = zeros(T+1,1)
X(1) = 10;
iter=0
while (abs(X(T+1)) > TOL);

What is T supposed to represent? The maximum number of iterations or something else? Should you increment it on each iteration of the while loop? See how X is a 6x1 array of zeros except for the first element which is 10. Then, in the condition for the loop, you are accessing the sixth element (since T is five) of X which is zero...which is less than TOL and so you never enter the loop.

If X is supposed to represent all of the outputs on each iteration of the loop, then you probably want to initialize T to be one and then increment on each iteration and setting X(T) to be some value...but that will conflict with this code

    for i = 1:T-1;
        X(i+2,1) = A * (1 + ALPHA * BETA)* (X(i+1,1))^ALPHA + (1-DELTA) * (1 + BETA) * X(i+1,1)...
            - BETA * (A * (X(i,1))^ALPHA + (1 - DELTA) * X(i,1)) * (A * ALPHA * X(i+1,1)^(ALPHA - 1) + (1 - DELTA));
    end;

Perhaps this the shooting part of the algorithm (which I don't understand). Please use the debugger or add some comments to your code which describe what is being attempted.

[heidi pham]

Thank you so so much.

I see what is wrong now: "which is less than TOL and so you never enter the loop."

that's why i got the result is 0 for all element of X.

I just meant to allocate memory by puting X a vector of zeros, then update it. But it causes the error as you pointed down.

I will revise my code and redo it to see if it goes well.

Thank you again!