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)

1. Solve by Gauss-Seidal iteration method
2. 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 :

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.

 

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

1000 500 0 0