We observed above that the solution of the simple system The purpose of this exercise is to derive a similar property for the system (a)    Show that where F and S solve (3.74). (b)   Integrate (3.75)...

We observed above that the solution of the simple system

The purpose of this exercise is to derive a similar property for the system

(a)    Show that

where F and S solve (3.74).

(b)   Integrate (3.75) from 0 to t and show that

(c)    Show that

(d)   Choose F₀
= 1.9, S0 = 0.1, and define the constant

Extend your program from Exercise 3.1 to compute

and generate a plot of
Argue that Kn seems to converge toward a constant, for all n, as t becomes smaller.

(e)   Let t = 10/N. Use the program you developed in (d) to compute