Interpolation and Curve Fitting - Numerical Methods in Engineering with MATLAB - page 124

14. Write a computerprogram forinterpolationbyNeville's method. The program
must be able to compute the interpolant atseveral user-specifiedvalues of x . Test
the program by determining y at x = 1 . 1, 1 . 2 and 1 . 3 from the following data:

x − 2 . 0 − 0 . 1 − 1 . 5 0 . 5

y 2 . 2796 1 . 0025 1 . 6467 1 . 0635

x − 0 . 6 2 . 2 1 . 0 1 . 8

y 1 . 0920 2 . 6291 1 . 2661 1 . 9896

4693)
15. The specificheat c p of aluminum dependson temperature T as follows: 4

(Answer: y = 1 . 3262, 1 . 3938, 1 .

T ( ◦ C) − 250 − 200 − 100 0 100 300

c p (kJ/kg · K) 0 . 0163 0 . 318 0 . 699 0 . 870 0 . 941 1 . 04

200 ◦ C and 400 ◦ C. Determine c p at T =

16. Find y at x = 0 . 46 from the data

x 0 0 . 0204 0 . 1055 0 . 241 0 . 582 0 . 712 0 . 981

y 0 . 385 1 . 04 1 . 79 2 . 63 4 . 39 4 . 99 5 . 27

17. The table shows the drag coefficient c D of a sphere as a function of Reynolds
numberRe. 5 Use naturalcubicsplinetofind c D at Re = 5, 50, 500 and 5000 . Hint :

use log-log scale.

Re 0 . 2 2 20 200 2000 20 000

c D 103 13 . 9 2 . 72 0 . 800 0 . 401 0 . 433

18. SolveProb. 17 using a polynomial interpolant intersecting four nearest-
neighbordatapoints.
19. The kinematic viscosity µ k of water varies with temperature T in the following

manner:

4

Source:Black, Z.B., and Hartley,J.G., Thermodynamics ,Harper & Row, 1985.

5

Source: Kreith, F. , Principles of Heat Transfer ,Harper & Row, 1973.