How to iterate a differential equation in matlab?

I need to iterate a differential equation until the output (the value of p) converges. Here is the code I wrote;

 threshold = ((zeros(1,2048)));
 old = p;
 new = zeros(1,2048);

 while norm( old-new) > threshold

    old = p;

    p = ((p * StateTransitionbwd) - (dd .* p));

    new = p;

end

In the equation I am using dp/dt as p. Do you know how should I treat this differential equation and what should I change in my code?

Thanks a lot.

Answer 1

[Walter Roberson]

http://uk.mathworks.com/matlabcentral/answers/235646#comment_306039

Also note that norm() is non-negative, and you are comparing for > zeros(), so the loop is not going to terminate until the two values are identical in every component, not just close. That is not a good idea: due to numeric roundoff you can get into cycles when you get really really close, alternately overshooting and undershooting, never exactly equal.

Mind you, norm() of a vector is a scalar and you are comparing a scalar to a vector of zeros. That is going to result in a vector of results the same length as the zeros(), with each element identical. The result would be the same as if you were testing against a single 0.

[Salman Saeed]

http://www.mathworks.com/matlabcentral/answers/235646#comment_306769

I have changed the norm to

while all(abs(old-new) > threshold)

I hope this will be fine as I want all of my elements in vectors to stop when they converge. Moreover please have a look at the link where I have attached a paper.