Hall Ticket No Question Paper Code: BST003
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Supplementary) February, 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 system of equations with partial pivoting.

x1 x2 3x3 3
2x1 x2 4x3 7
3x1 5x2 2x3 6
Use the Givens method to find the Eigen values of the matrix 2
6664
2 0
2
0 2
3
7775

2. Use the triangular method to solve the following simultaneous linear equations.
2
6664
25 5 1
64 8 1
144 12 1
3
7775
2
6664
a1
a2
a3
3
7775

2
6664
106:8
177:2
279:2
3
7775
Solve the following linear system of equations using by Jacobi method rounded to four decimal
places.
10x1 x2 2x3 6
x1 11x2 x3 3x4 25
2x1 x2 10x3 x4
3x2 x3 8x4 15
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UNIT II
3. A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a 15001000
rectangular plate. The centers of the holes in the plate describe the path the arm needs to take,
and the hole centers are located on a Cartesian coordinate system (with the origin at the bottom
left corner of the plate) given by the specifications in Table 1.
Table 1
x(in.) 2.00 4.25 5.25 7.81 9.20 10.60
y(in.) 7.2 7.1 6.0 5.0 3.5 5.0
Find the path traversed through the six points using a fifth order Lagrange polynomial.
Construct Newtons forward difference interpolating polynomial for the following data given in
Table 2 hence evaluate
Table 2
x 0 1 2 3
1 2 1 10
4. Given the following values of and f0 estimate the values of using the Hermite
interpolation
Table 3
x f0
1
1 3 7
For linear interpretation, in the case of equispaced tabular data, shows that the error does not
exceed 1/8 of the second difference.
UNIT III
5. A rod is rotating in a plane. The Table 4 below gives the angle (in radians) through which the
rod has turned for various values of the time t (in seconds).
Table 4
t 0 0.2 0.4 0.6 0.8 1.0 1.2
0 0.12 0.49 1.12 2.02 3.20 4.67
Calculate the angular velocity when t=0.6.
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Compute f0 from the following Table 5 using appropriate interpolating polynomial
Table 5
x 1 2 4 8 10
0 1 5 21 27
6. By repeated application of Richardson extrapolation find f0 from the following Table 6 values.

Table 6
x 0.6 0.8 0.9 1.0 1.1 1.2 1.4
0.707178 0.859892 0.925863 0.984007 1.033743 1.074575 1.127986
Use the formula
2h and h=0.4,0.2,0.1.
Find f by applying central difference formula given that f =0.2707, f =0.3027,
f =0.3386, f =0.3794.
UNIT IV
7. For the method 1
6 +RE determine the optimum
value of H using the criteria jREj jTEj, where TE and RE are respectively the truncation
error and round error.
Find the jacobian matrix for the system of equations
x2 y2 x 0
x2 y2 y 0 at the point using the second order differentiation method.
8. A solid of revolution is formed by rotating about X-axis, The area between the X-axis and the
lines x=0 and x=1 is a curve through the points with the following coordinates shown in Table
7.
Table 7
x 0 2.5 5.0 7.5 10.0 12.5 15.0
y 5 5.5 6.0 6.75 6.25 5.5 4.0
Estimate the volume of the solid so generated.
Determine a,b and c such that the formula
R h
0 f(x)dx hfaf(0) bf(h
3 cf(h)g is exact for
polynomial of as high order as possible.
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UNIT V
9. Using Euler's method solve for y at x=2 from y0 3x2 2 taking h=0.25
Apply the fourth order Runge Kutta method to find y at x=1.2 from y0 x2 y2; 1:5
taking h=0.1
10. Solve the boundary value problem u00 0 x by using shooting
method.
given the boundary value problem 0:5 apply the cubic spline
method to determine the value of y (1.5).
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