Absolute stability question -

[elle]

Absolute stability question - urgent!

Hi, I wasn't too sure what section to put this in but I'm currently working on an exercise regarding absolute stability in the class Numerical Solutions of ODEs. Here is the graph i have produced on Matlab and I am suppose to comment on it. The graph shows the exact solution (black line) and the approximate solution of the given method with N = 70 when it is just stable.

http://i16.tinypic.com/2e5ky0l.jpg"

So far, I have made the comments that it can be observed that there is decreasing saw-tooth solution with smaller errors. For any values above N = 64, the errors will continue to decrease and the solution eventually converging.

But I don't know if I am on the right track, can anyone help me out? Any additional comments I have left out would be helpful!

 

[LeBrad]

Hi, I wasn't too sure what section to put this in but I'm currently working on an exercise regarding absolute stability in the class Numerical Solutions of ODEs. Here is the graph i have produced on Matlab and I am suppose to comment on it. The graph shows the exact solution (black line) and the approximate solution of the given method with N = 70 when it is just stable.

http://i16.tinypic.com/2e5ky0l.jpg"

So far, I have made the comments that it can be observed that there is decreasing saw-tooth solution with smaller errors. For any values above N = 64, the errors will continue to decrease and the solution eventually converging.

But I don't know if I am on the right track, can anyone help me out? Any additional comments I have left out would be helpful!

It would be helpful if you gave a few more details here. First, when you say stability, are you referring to the stability of a critical point of a differential equation, or the stability of a numerical method for solving a differential equation? Second, what method are you using to solve the equation? What is N? Is it the number of time points in the interval? Do you know the definition for stability of a numerical time-integration scheme?