B.E-B.E Applied Numerical Methods(Sathyabama University, Chennai, Tamil Nadu-2011)
Monday, 19 August 2013 08:31Duraimani
(Established under section 3 of UGC Act,1956)
Course & Branch :B.E/B.Tech - P-CIVIL/P-ECE/P-EEE/P-MECH/P-CHEM
Title of the Paper :Applied Numerical Methods Max. Marks:80
Sub. Code :SMTX1011(2010) Time : 3 Hours
Date :01/11/2011 Session :AN
PART - A (10 x 2 = 20)
Answer ALL the Questions
1. Fit a straight line for the following data:
| x |
0 |
1 |
3 |
| y |
4 |
8 |
5 |
2. Prove that E = 1 + D
3. If f(x) is given by
| x |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |
| f(x) |
6 |
4.5 |
2.9 |
1.9 |
1.1 |
0.6 |
0 |
4. Distinguish between interpolation and extrapolation.
5. What is the first approximation interval of the equation
6. Solve the following equations by Gauss-Jordan method
x + y = 2 and 2x + 3y = 5.
7. Write down the Milline’s predicator-corrector formula to solve a first order differential equation.
8. Find the Taylor’s series expansion of y = ex about x = 0.
9. Classify the following equation for
10. Write down the standard five point formula and diagonal five point formula.
PART – B (5 x 12 = 60)
Answer ALL the Questions
11. Fit a parabola y = ax2 + bx + c for the following data:
| x |
0 |
2 |
4 |
6 |
8 |
10 |
| y |
1 |
3 |
13 |
31 |
57 |
91 |
12. (a) Find the nth difference of ex.
(b) Prove that E = ehD.
13. Using Lagrange’s method find the value of y when x = 8 for the following data:
| x |
5 |
9 |
11 |
12 |
| y |
121 |
73 |
25 |
26 |
14. Evaluate using
(a) Simpson’s rule and (b) Simpson’s with h = 1.
15. Using Ragula-Falsi method find the positive root of
(or)
16. Solve by using Gauss-Jordan method
5x – 2y + 3z = 18
x + 7y – 3z = -22
2x – y + 6z = 22
17. Using Taylor’s series method find y at x = 1.1, correct to 3 decimal places from with y(1) = 2.3.
(or)
18. Solve by Modified Euler’s method by finding y for x = 0(0.1) 0.2,
19. Solve the equation with the following boundary and initial conditions with h = 3 and k =3.
using Schmidt relation.
(or)
20. Solve uxx + uyy = 0 in Given that
u(0, y) =0
u(4, y) = 8 + 2y
u (x, 4) = 2
taking h = k = 1. Obtain the result correct to one decimal.
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