Hall Ticket No Question Paper Code: BST003
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) February, 2017
Regulation: IARE-R16
COMPUTER ORIENTED NUMERICAL METHODS
(Structural Engineering)
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 linear equations with partial pivoting
x1 x2 3x3 3
2x1 x2 4x3 7
3x1 5x2 2x3 6
Use Householder's method to convert the matrix
2
6666664
4 1 2
1 2 0 1
0 3
2 1
3
7777775
into tridiagonal form.

2. 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
Find the largest eigen value and corresponding eigen vector of the matrix
2
6664
1:5 0 1
0:5
0 0
3
7775
by using power method.
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UNIT II
3. Using Newton divided differences, construct the interpolating polynomial for the data set given
below
i 1 2 3 4 5
x 0 5 7 8 10
y 0 2 20
The upward velocity of a rocket is given as a function of time in the following Table.
0 10 15 20 22.5 30
0 227.04 362.78 517.35 602.97 901.67
Determine the value of the velocity at t=16 seconds with third order polynomial interpolation using
Lagrangian polynomial interpolation.
4. Construct the free cubic spline to approximate f cos by using the values given by f at x
0:75 and 1:0
UNIT III
5. Using the formula f0
2h and Richardson extrapolation find f0 (3)from the following
table values.
x 1 2 3 4 5 7
1 1 16 81 256 625 2401
Given the values of f ln x find the approximate values of f0 and f00 using
quadratic interpolation and also obtain an upper bound on the error.
x 2.0 2.2 2 .6
0.69315 0.78846 0.95551
6. Find the maximum and minimum values from the following table
x 0 1 2 3 4
2 -0.25 0 -0.25 2 15.75 56
UNIT IV
7. Estimate the values of
at
at using first order formula and @2f
at
using second order formula from the following table values.
x 0.1 0.2 0.3
0.1 2.02 2.0351 2.0403
0.2 2.0351 2.0801 2.1153
0.3 2.0403 2.1153 2.1803
For the method f0
2h h2
3 f000 x0 x2 determine the optimum
value of h using the criteria jREj jTEj.
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8. Evaluate the integral
R2
1
R2
1
dxdy
x+y using trapezoidal rule with h k 0:5 and h k 0:25. Improve
the estimate using Romberg Integration.
UNIT V
9. Apply Euler's method with step sizes h 0:2 and 0:15 to compute approximations to y(0.6)
by solving ordinary differential equation y0 x y 2
Using RK method of order 2 compute y from y0
x y taking h 0:25
10. Solve boundary value problem u00 u u u 0 with h 1/4
Solve by Taylor's series method the equation y0 log y 2 for y and y
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