Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Numerical methods - Question Paper
MODEL EXAMINATION
NUMERICAL METHODS
Year/Branch/Sem : II / EEE / IV Marks: 100
PART-A (20 X 2 = 40)
- Solve by Gauss-Seidal iteration method
- Compare Gauss-Jacobi & Gauss-Seidal methods for solving a linear
system of the form .
3. Say True (or) False. Iteration method is a self-correction method.
4. Define Round-off error.
5. What is the Lagranges formula to find y ,if three sets of values of values are given?
6. Give the Newtons divided difference interpolation formula.
7. State Gregory-Newton forward difference interpolation formula
8. Using Newtons divided difference formula find the missing value
from the table :
x |
1 |
2 |
4 |
5 |
6 |
y |
14 |
15 |
5 |
- |
9 |
9. State Newtons formula to find using forward differences
10. State Simpsons three eighth rule.
11. In order to evaluate by Simpsons 1/3 rule as well as by Simpsons 3/8 rule ,What is the restriction on the number on intervals
12. State two point Gaussian quadrature formula to evaluate
13. Write down the fourth order Taylor Algorithm .
14. Using Modified Eulers method, find y(0.1) if
15. Compare Taylors series and R.K.Method.
16. What are the values of and to solve by Runge-Kutta method of fourth order.
17. What is the classification of one dimensional heat flow equation?
18. Write down the finite difference form of the equation .
19. What type of equations can be solved by using Crank-Nicolsons difference formula ?
20. State Schmidts explicit formula for solving heat flow equation.
PART-B (ANY 5 ) (5 X 12 = 60)
21. a)Find the real positive root of by Newtons
method correct to 6 decimal places.
b) Using Gauss-Jordan method , solve the following equations
.
22. a)Using Gauss-Jordan method ,find the inverse of .
b) Using Newtons forward interpolation formula, find the polynomial
f(x) satisfying the following data.
x: |
0 |
5 |
10 |
15 |
y: |
14 |
379 |
1444 |
3584 |
23. Using Newtons divided difference formula, find u(3) given
u(1)=-26,u(2)=12,u(4)=256,u(6)=844.
24. Find and for the following data :
x |
3.0 |
3.2 |
3.4 |
3.6 |
3.8 |
4.0 |
f(x) |
-14 |
-10.032 |
-5.296 |
-0.256 |
6.672 |
14 |
25. a)Using trapezoidal rule ,Evaluate taking 8 intervals.
b)Evaluate by using three point Gaus quadrature formula
26. a) Using Eulers method find the solution of the initial value problem
by assuming h=0.2.
b)Using modified Eulers method, compute y(0.1) with h=0.1 from
27. Find y(0.8) given that by using Runge-Kutta method of fourth order. Take h=0.1.
28. Obtain a finite difference scheme to solve the Laplace equation
Solve at the pivotal points in the square shown fitted with
square mesh. Use Leibmanns iteration procedure.(5 iteration).
1000 1000 1000 1000
|
u1 |
u2 |
|
u3 |
u4 |
|
|
|
1000 500 0 0
Earning: Approval pending. |