Numerical Methods BPUT Questions

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Numerical method BPUT university…

Question paper:

ANSWER ALL QUESTIONS
1. Find 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. Find the dominant Eigen value of A = ?
?
?
??
?
3 4
1 2 by power method

5. State the Lagrange's interpolation formula.

6. Write the divide difference table for the following data
X 2 5 10
y 5 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 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 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

ANSWER ANY FIVE QUESTIONS

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 find the eigen value of 1 3 3 4

23. The table givesb the distance in nautical miles of the visible
horizon for 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 ? ?
6
0
1 x2
dx using simpson 1/3rule

25.evaluate?????.???????.??1/???? by simpson rule and verify by actual
integration

26. a.Using modified Euler's method, find y(0.25) if ? 2xy , y(0) ? 1
dx
dy .
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 euler method
(ii)y(0.3) by modified euler method
(iii)y(0.4) by milne's method

28. Solve u xx + u yy = 0 over the square mesh of side 4 units, satisfying
the following
conditions .
u(x,0) =3x for 0? x ? 4
u(x, 4) = x 2 for 0? x ? 4
u(0,y) = 0, for 0? y ? 4
u(4,y) = 12+y for 0? y ? 4