Please just explain if the problem is stiff and explain why or why not. If it is

Question

Please just explain if the problem is stiff and explain why or why not. If it is stiff in one part and not in the other, explain. Please show all work.

Thank you

(2 points each part) Are the following initial value problems stiff? Ex plain why or why not. In case a problem is stiff in one part of the time interval and nonstiff in another part, identify the approximate time in- tervals over which it is stiff or nonstiff, respectively. Assume an error tolerance of 10 (c) y,=-106(y-sin(10%)) + cos( 100t), te l0.1), yo=0

Explanation / Answer

A differential equation of the form y'=f(t,y) is said to be stiff if its exact sol y(t) includes a term that decay exponentially to zero when t increases,but whose derivatives are much greater in magnitude than term itself.An example of such a termis e-ct where c is a large,because kth derivatives is cke-ct

part(a) the given differential equation is non stiff as the exact sol of this is of type ce^-106t which dont decay exponentially to zero wiith time because when you put t=10-6 you get the sol c/e

part(b) in this part equation will be stiff as its exact sol decays exponentially zero with time.

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