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EECS 328:
Numerical Methods for Engineers

Department of Electrical Engineering and Computer Science

Northwestern University

Spring 2009

Weekly Problem Set #8

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Due Time:

The written problems should be
turned in on paper at the start of class on Friday, 6/5/2009.
The programming assignments should
be deposited in the Blackboard Digital Dropbox before the class on Friday,
6/5/2009.

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Written Problems:

- (12.5 points) Exercise 9.1 on page
416.
- (12.5 points) Exercise 9.4
on page 417.
- (12.5 points) Exercise 9.5
on page 417. Also compute the solution values y
_{2} and y_{3}
for t_{2} = 2 and t_{3 }= 3.
- (12.5 points) Find a
predictor for the ODE y' = f(t, y) of the form y
_{k+1} = w_{0}y_{k}+w_{1}y'_{k}+w_{2}y_{k-1}+w_{3}y_{k-2}.
Use the method of undetermined coefficients to determine the coefficients w_{0},
w_{1}, w_{2}, and w_{3} by forcing the predictor to
be exact for the first four monomials, 1, t, t^{2}, and t^{3}.

**Programming Assignments:**
Write your programs in Matlab. Turn in both the programs and the outputs.
Organize the outputs neatly and comment them.

- (25 points) Computer
Problem 9.1(a) on page 418.
- (25 points) Computer
Problem 9.2 on page 418.