Anna University Coimbatore 2011 B.E Civil Engineering Numerical methods 080280026 - Question Paper

ANNA UNIVERSITY COIMBATORE
B.E/B.TECH.DEGREE EXAMINATIONS: MAY/JUNE 2011
REGULATIONS: 2008
THIRD SEMESTER: CIVIL /EEE/AERO
080280026-NUMERICAL METHODS
Time: three Hours Max.Marks:100
PART-A
(20X2=40MARKS)
ans ALL ques.
1. obtain iterative formula for 1/N where N is a positive integer, by
Newton's method.
2. By Gauss Jordan method, solve x+y=2, 2x+3y=5.
3. Compare Gauss Elimination and Gauss Siedel methods
4. obtain the dominant Eigen value of A = ?
?
?
??
?
3 4
1 two by power method
5. State the Lagrange's interpolation formula.
6. Write the divide difference table for the subsequent data
X two five 10
y five 29 109
7. What do you mean by interpolation?
8. What is the advantage of Lagrange's formula over Newton's
formula.
9. Write the formula for dy/dx at x=x0 using Newton forward
difference
10. What the errors in Trapezoidal and Simpson's rule.
11. When the simpson rule provide the exact outcome
12. Write the formula for trapezoidal rule double integration.
13. State the disadvantage for taylor's series method.
14. By eulers method obtain the y(1.1)given y'=x+y , y(0)=0
15. Compare taylor series and runge kutta method
16. Write down the adamns predictor and corrector formula
17. Write down the standard 5 point formula used in solving
laplace formula Uxx + U yy = 0 at the point
18. What is the value of k used to solve ðu/ðt =0.5ð2u/ðx2 by
bender schmit method with h=1 if h and k are the increments of x
and t respectively?
19. Derive Crank-Nicolson scheme.
20. State Bender Schmidt's equations
PART B
ans ANY 5 ques.
5x12=60 MARKS
21.a]find real positive root for 3x-cosx-1=0 by Newton's method
[b]solve 2x+3y-z=5 4x+4y-3z=3 2x-3y+2z=2 by gauss elimination
method
22.a) Solve the system of equations using Gauss Seidel iterative
methods.
28x +4 y – z = 32, x + 3y +10 z =24 , 2x +17y +4z = 35.
(b)using Jacobi method obtain the eigen value of one three 3 4
23. The table givesb the distance in nautical miles of the visible
horizon for the provided heights in feet above the earth surface
X=height 100 150 200 250 300 350 400
Y=distance 10.63 13.03 15.04 16.81 18.42 19.90 21.27
obtain the values of y when x=218 x=410
24.the salese of theb certain town is provided beneath obtain the rate of sales
in 1931
Year 1931 1941 1951 1961 1971
Sales in
thousands
40.02 60.08 79.95 103.56 132.65
Evaluate ? ?
6
0
1 x2
dx using simpson 1/3rule
25.evaluate?????.???????.??1/???? by simpson rule and verify by true
integration
26. a.Using replaced Euler's method, obtain y(0.25) if ? 2xy , y(0) ? 1
dx
dy .
b. calculate y(0.1) provided y'=-y y(0)=1 by RK method
27. provided y'=1-y y(0)=0 obtain
(i ) y(0.1) & y(0.2) by euler method
(ii)y(0.3) by replaced euler method
(iii)y(0.4) by milne's method
28. Solve u xx + u yy = 0 over the square mesh of side four units, satisfying
the subsequent
conditions .
u(x,0) =3x for 0? x ? 4
u(x, 4) = x two for 0? x ? 4
u(0,y) = 0, for 0? y ? 4
u(4,y) = 12+y for 0? y ? 4

10.    What the errors in Trapezoidal and Simpson's rule.

11.    When the simpson rule give the exact result

12.    Write the formula for trapezoidal rule double integration.

13.    State the disadvantage for taylor's series method.

14.    By eulers method find the y(1.1)given y'=x+y , y(0)=0

15.    Compare taylor series and runge kutta method

16.    Write down the adamns predictor and corrector formula

17.    Write down the standard five point formula used in solving laplace equation U + U = 0 at the point

18.    What is the value of k used to solve 5u/5t =0.55²u/5x² by

bender schmit method with h=1 if h and k are the increr and t respectively?

19.    Derive Crank-Nicolson scheme.

20.    State Bender Schmidt's equations

PART B ANSWER ANY FIVE 5x12=60..... _{s (}

21.a]find    real positive root for 3x-cosx-1=u by Newton's method

../.vr.v..... m ilk.

:|r

[b]solve 2x+3y-z=5 4x+4yp5z=r method

22.a)    Solve the system Jlations using Gauss Seidel iterative methods.

28x+4 y -* = 32, x + 3y +10 z =24 , 2x +17y +4z = 35.

jobr method find the eigen value of 1 3 3 4

23. The: fable givesb the distance in nautical miles of the visible horizonfor the given heights in feet above the earth surface

X=height 100 150 200 250 300 350 400 Y=distance 10.63 13.03 15.04 16.81 18.42 19.90 21.27

Find the values of y when x=218 x=410

24.the salese of theb certain town is given below find the rate of sales in 1931

Year 1931 1941 1951 1961 1971 Sales in thousands 40.02 60.08 79.95 103.56 132.65

Evaluate Jusing simpson 1/3rule

25.evaluate/₁¹' ⁴ J₂²'⁴1/xy by simpson rule and verify by ictdc

_if ¹

.²⁵).... ft.- 2^xy

b. compute y(0.1) given y'=-y y(0)=1 by "RK....method 27. given y'=1-y y(0)=0 find (i ) y(0.1) & y(0.2) by eulr met

(ii)y(0.3)    by modified.!! ethod

(iii)y(0.4)    by milns" thod

over the square mesh of side 4 units, satisfying

u(0,y) = 0,    for 0 < y < 4

Attachment: anna-university-coimbatore-2011-b-e-civil-engineering-668-1.pdf

Earning:   Approval pending.