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<div class="moz-cite-prefix">On 11/2/23 16:28, David M. Hunt wrote:<br>
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cite="mid:facaab801e0d451eb74941c9be500150@SA1PR01MB6528.prod.exchangelabs.com">
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<p class="MsoNormal">Hi,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">In questions Section 5.9 problems #5 and #6
both request find a stable solution. What is meant by
stable? Thanks.<o:p></o:p></p>
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<p><font face="serif">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). <br>
</font></p>
<p><font face="serif">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.<br>
</font></p>
<img moz-do-not-send="false"
src="cid:part1.4DNZfDqf.wPVC7gat@mercer.edu" alt="example1"
width="640" height="480"> <img moz-do-not-send="false"
src="cid:part2.0mkxdiuF.10AQ0HHr@mercer.edu" alt="stable"
width="640" height="480">
<div class="moz-signature">-- <br>
<b><i>Andrew J. Pounds, Ph.D.</i></b><br>
<i>Professor of Chemistry and Computer Science</i><br>
<i>Director of the Computational Science Program</i><br>
<i>Mercer University, Macon, GA 31207 (478) 301-5627</i></div>
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