Hall Ticket No Question Paper Code: BST003
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Supplementary) July, 2018
Regulation: IARE-R16
COMPUTER ORIENTED NUMERICAL METHODS
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Solve the following equations using Gauss seidel iteration method. 2x+3y=5.

Solve the following equations using Gauss Jordan method. x y 2 x y 5
2. Solve the following equations using relaxation method.

x+10y-2z=15;
2x-2y-13z=17
Show that LU decomposition method fails to solve the system of equations. 2
UNIT II
3. Find the Lagrange's interpolating polynomial of degree 2 approximating the function y=ln
x defined by the following table of values. Hence determine the value of ln 2.7
x y=ln x
2.0 0.69315
2.5 0.91629
3.0 1.09861
Construct the free cubic spline to approximate cosx by using the values given by
f at x 0:75 and 1:0.
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4. For linear interpretation, in the case of equispaced tabular data, show that the error does
not exceed 1/8 of the second difference.
Determine the natural cubic spline s which approximates the below Table the
function z=f satisfies the following data for 0 Y Z. Find the approximate value
of z (0.5,0.5).
Table 1
X
Y 0 1 2
0 1 2 9
1 2 3 10
2 9 10 17
UNIT III
5. If 246; 202; 118; Find y(79).
Find the cubic polynomial which takes the following values shown in Table 2.
Table 2
x 0 1 2 3
1 2 1 10
6. Find by applying central difference formula given that
f =0.2707, f =0.3027, f =0.3386, f =0.3794.
Find the value of x correct to one decimal place for which y=7 for the given data shown
in
Table 3.
Table 3
x 1 3 4
y 4 12 19
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UNIT IV
7. Evaluate
R1
0
dx by dividing the range into 4 equal parts using Trapezoidal rule.
A rod is rotating in a plane as shown in Table 4 which gives the angle through which
the rod has turned for various values of time t sec.
Table 4
t 0 0.2 0.4 0.6 0.8 1.0
0 0.12 0.49 0.49 2.02 3.20
Calculate the angular velocity and the angular acceleration of the rod when t=0.6 sec.
8. Find the value of log 21/3 from
R1
0
x2
1+x2 dx using simpson's 1/3 rule with h=0.25.
Find at x=0.5 for the given data shown in Table 5
Table 5
x 0 1 2 3 4
1 1 15 40 85
UNIT V
9. From the Taylor series for y find y correct to 4 decimal places if satisfies.
y1 x y2, and y =1.
Solve the equation subject to the condition y=1 when x=0.
10. Solve the boundary-value problem @2y
0 with y y 3.62686
Given the boundary value problem x2y11 xy1 y 0:5 apply the
cubic spline method to determine the value of y (1.5).
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