1. Computational Methods Autar Kaw University of South Florida
Bring it together
Computational Methods
Autar Kaw
University of South Florida

2. Why Do We Use Numerical Methods?

3. Why use Numerical Methods?
To solve problems that cannot be solved exactly

4. Why use Numerical Methods?
To solve problems that have exact solutions but are otherwise intractable!

5. A Bascule Bridge Opening

6. Bascule Bridge THG

7. Bascule Bridge THG
Hub
THG picture
Trunnion
Girder

8. Trunnion-Hub-Girder Assembly Procedure
Step1. Trunnion immersed in dry-ice/alcohol
Step2. Trunnion warm-up in hub
Step3. Trunnion-Hub immersed in
dry-ice/alcohol
Step4. Trunnion-Hub warm-up into girder

9. After Cooling, the Trunnion Got Stuck in Hub
Problem
After Cooling, the Trunnion Got Stuck in Hub

10. Why did it get stuck?
Magnitude of contraction needed in the trunnion was 0.015” or more. Did it contract enough?

11. Video of Assembly Process

12. What model should I use to calculate contraction of trunnion?

13. Finding the fluid temperature to get enough contraction

14. Finding the expression for thermal expansion coefficient

15. What is the temperature of the trunnion after half an hour?

16. How long does it take a trunnion to cool down?

17. What is the rate of change of heat stored in the cylinder?

18. Using central divided difference, the true error in the calculation of a derivative of a function is 32.0 for a step size of If the step size is reduced to 0.1, the true error will be approximately
2.0
4.0
8.0
16.0

19. Given the f (x) vs x curve, and the magnitude of the areas as shown, the value ofy x a 5 7 2 b c -2 2 12
Cannot be determined

20. A scientist finds that regressing y vs x data given below to straight-line y=a0+a1x results in the coefficient of determination, r2 for the straight-line model to be one. x 1 3 11 17 y 2 6 22 ?
The missing value for y at x=17 most nearly is
-2.444
2.000
6.889
34.00

21. The distance covered by a rocket from t=8 to t=34 seconds is calculated using multiple segment trapezoidal rule by integrating a velocity function. Below is given the estimated distance for different number of segments, n. n 1 2 3 4 5
Value
16520
15421
15212
15138
15104
The number of significant digits at least correct in the answer for n=5 is 1 2 3 4

22. Polynomials are most commonly used functions for interpolation because they are easy to
evaluate
differentiate
integrate
all of the above

23. Using 3 significant digit with chopping at all stages, the result for the following calculation is

24. The velocity of a body is given by
Then the distance covered by the body from t=0 to t=10 can be calculated by solving the differential equation for x(10) for A) B) C) D)

25. The root of equation f (x)=0 is found by using Newton-Raphson method
The root of equation f (x)=0 is found by using Newton-Raphson method. The initial estimate of the root is xo=3, f (3)=5. The angle the tangent to the function f (x) at x=3 makes with the x-axis is 57o. The next estimate of the root, x1 most nearly is
3.2470
6.2470

26. Resources http://nm. MathForCollege. com http://YouTube
Resources Contact:

27. THE END