[CSC 335] HW 5

[Andrew J. Pounds]

On 11/2/23 16:28, David M. Hunt wrote:
>
> Hi,
>
> In questions Section 5.9 problems #5 and #6 both request find a stable 
> solution.  What is meant by stable?  Thanks.
>
While a full explanation of stability with respect to initial value 
problems in differential equations would require more than an email (I 
think it is section 5.10 in your text),  the short answer is that a 
stable solution will produce small changes in the output based on small 
changes in the input.  In other words there is a clear dependence on the 
output based on the input.  Another definition that is often inferred 
when solving problems numerically is that stable solutions are 
convergent (don't go to plus or minus infinity or display erratic 
behavior).

However, in problems 5 and 6 it is asking about population stability -- 
which means that the populations basically stay constant. The two graphs 
below show what one normally expects for a predator-prey solution, the 
second one shows what happens when a stable solution is found.  There is 
also a BIG hint in the second graph that could help you with the homework.

example1 stable
-- 
*/Andrew J. Pounds, Ph.D./*
/Professor of Chemistry and Computer Science/
/Director of the Computational Science Program/
/Mercer University, Macon, GA 31207 (478) 301-5627/
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