ALCCS
FEBRUARY 2009
NOTE:
· Question 1 is compulsory and
carries 28 marks. Answer any FOUR questions from the rest. Marks are indicated against each question.
· Parts of a question should be
answered at the same place.
· All
calculations should be up to three places of decimals.
Q.1 (7
x 4)
a. Find the relative error in the
function
b. Perform two iterations to find
the fourth root of 32, using the method
of false position.
c. Factorize the
matrix using LU
decomposition.
d. Determine the
largest eigenvalue in the fourth approximation and its corresponding
eigenvector of the matrix using Power method.
e. Apply Gauss
Jordan method to solve the equations AX=B where ,
f. Find
g.
Solve at 0.1 using
Euler method.
Q.2 a. Find the root of xex=3 by
Regular falsi method correct to three decimal places. (9)
b. Find the missing values in the following table
of values of x and y: (9)
x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
y |
-4 |
-2 |
---- |
--- |
220 |
546 |
1148 |
Q.3 a. Find the inverse of by Crout’s
method. (9)
b. Using Given’s Method, reduce the following
matrix to the tri-diagonal form: (9)
A=
Q.4 a. Solve by Gauss elimination method, the following system of
equations: (9)
b. Determine the order of convergence of the
iterative method for finding a simple
root of the equation f(x)=0. (9)
Q.5 a. The following table gives the values of
density of saturated water for various temperatures of saturated steam.
T=temp0
C |
100 |
150 |
200 |
250 |
300 |
d
= density (hg/m3) |
958 |
917 |
865 |
799 |
712 |
Find
by
b. Use
Lagrange’s interpolation formula to find the value of y when x = 10, if the
values of x and y are given as below: (9)
x |
5 |
6 |
9 |
11 |
y |
12 |
13 |
14 |
16 |
Q.6 a. The population of a certain town is shown in
the following data: (9)
Year |
1951 |
1961 |
1971 |
1981 |
1991 |
Population (in thousands) |
19.96 |
36.65 |
58.81 |
77.21 |
94.61 |
Find the rate of growth of the population
in the year 1981, using
b. The velocity v of a particle at a distance s
from a point on its path is given by the following table: (9)
s(ft) |
0 |
10 |
20 |
30 |
40 |
50 |
60 |
v (ft/s) |
47 |
58 |
64 |
65 |
61 |
52 |
38 |
Estimate
the time taken to travel 60 ft using Simpson’s 1/3 rule.
Q.7 a. Using Runge-Kutta method of fourth order, solve for y(0.1), y(0.2)
given that . (12)
b. Using