Tamil Nadu Open University (TNOU) 2006 B.C.A Computer Application -12 COMPUTER ORIENTED NUMERICAL METHODS - - Question Paper

TAMILNADU OPEN UNIVERSITY

BCA DEGREE exam - JUNE 2006

BCA-12 COMPUTER ORIENTED NUMERICAL METHODS

UG-725    BCA-12

B.C.A. DEGREE EXAMINATION - JUNE 2006.

Second Year

(For Candidates admitted in AY-200405 only)

COMPUTER ORIENTED NUMERICAL METHODS

Time : 3 hours    Maximum marks : 60

PART A (4 x 5 = 20 marks)

Answer any FOUR questions.

1.    Perform 3 iterations of fixed point iteration method to find the smallest positive root of the equation.

x^z - 3x + 1 = 0 by starting at x₀ = 0.5.

2.    Explain Jacobis iterative method and sufficient condition for convergence of the Jacobi method.

3.    What is Inverse Interpolation? Find the value of x when y = 3.

x 4 7 10 12 Y -\ 1 2 4

4.    Prove the uniqueness of the interpolating polynomial by applying suitable results.

5.    Find Newtons backward difference form of interpolating polynomial for the data given below :

x 4 6 8 10

fix) 19 40 79 142

Hence interpolate f (9).

6.    Discuss briefly the various types of errors that will arise in numerical calculation.

PART B (4 x 10 = 40 marks)

Answer any FOUR questions.

7.    Perform three iterations of second method to solve x³ + x - 6 = 0. Starting with x₀ = 1 and x_x 2.

8.    Find the iteration function g ix) and corresponding interval to get the two roots 1 and 2 by fixed point iteration method for the equation x²-3x + 2 = 0.

9.    Solve the system of equations by Gauss elimination.

x_l - x₂ + 2x₃ - x₄ = - 8 2x_t - 2x₂ + 3x_a - 3x₄ = - 20 x_t + x₂ + x₃ + 0x₄ = - 2 x_x-x₂ + 4x₃ + 3x₄ = 4

10. Using forward differences show that the following data represents a third degree polynomial.

-3-2-1012 3

f{x) -29 -9-113 11 31

Find the polynomial and obtain the value of

/ (0.5).

11.    (a) Explain interpolation and extrapolation.

(b) Discuss briefly Lagranges form of interpolating polynomial.

12.    (a) State intermediate value theorem.

(b) Find a root by Bisection method which lies between 0 and 1.

at³ -5*+ 1 = 0.

3    UG-725

Attachment: tamil-nadu-open-university--tnou--2006-b-c-a-computer-application-48871-1.pdf

Earning:   Approval pending.