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ESC 251 HW 35 Due: Dec. 6
(15 pts) Recall that the standard 4th order RungeKutta
method for solving a first order initial value problem is given by
y(0) = yO
for i = 0,1,....
k1 = f(t(i),y(i))
k2 = f(t(i)+h/2,y(i)+h*k1/2)
k3 = f(t(i)+h/2,y(i)+h*k2/2)
k4 = f(t(i)+h,y(i)+h*k3)
y(i+1) = y(i) + h*(k1 + 2*k2 + 2*k3 + k4)/6
Write a main program and accompanying subroutines/functions
that will implement this method for solving the first order initial
value problem
Use your program to solve the following problems. In each case, determine
the value of n necessary for the 2norm of the error vector to
be less than 10^{6}. Use separation of variables or the Wolfram
Alpha site to determine the exact solutions.
 a)

How does the value of n for this problem compare to the one
for Euler's method?
 b)

 c)

What is different about the value of n you obtain for this problem? Why
do you think this is happening?
20171204