Page 285 - Excel for Scientists and Engineers: Numerical Methods

262 EXCEL: NUMERICAL METHODS

Problems

Answers to the following problems are found in the folder "Ch. 11 (BVP)" in the
"Problems & Solutions" folder on the CD.

1. Repeat the beam deflection example at the beginning of this chapter, using
the Runge-Kutta method instead of Euler's method. Use Goal Seek.. . to
solve the problem. What is the maximum beam deflection?

2. Modify the beam deflection example at the beginning of this chapter, so that
200 rows of calculation are performed, and the length of the beam L is a
variable. Use Goal Seek.. . to solve the problem. What is the maximum
beam deflection for a 400-in beam, the other parameters (w, E, I) remaining
constant?

3. Use the shooting method and Goal Seek.. . to solve
y" = x + (1 -x2)y
where y( 1) = 2 and y(3) = 0. Use the Runge-Kutta method to calculate y.

4. Use the shooting method and Goal Seek.. . to solve
29' - XY' + 3y = 3
where y(0) = 1 and y( 1) = -6. Use the Euler method to calculate y and y'

5. Use the shooting method and Goal Seek.. . to solve

y" - xy' + 3y = 0
where y(0) = 1 and u( 10) = 257. Use the Euler method to calculate y and y'.

6. Use the shooting method and Goal Seek.. . to solve
y" + xy' - 3y = 0
where y(-3) = -9 and y(7) = 9 1. Use the Euler method to calculate y and y'.

7. Repeat problem 3 using the Runge-Kutta method to calculate y and y'.