Numerical Analysis 2021 – BSc Computer Science Part 2

Total No. of Questions : 8] [Total No. of Printed Pages : 4

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2021
Paper No. 1.3
NUMERICAL ANALYSIS

Time: Hours] [Maximum Marks: 50

Note: Attempt all sections as directed.

Section-A

1. Attempt any two questions :15 each

   (a) Evaluate :

   (b) Find f(6) given that f(0) = -3, f(1) = 6, f(2) = 8, f(3) = 12, the third difference being constant.

2. (a) Use Newton formula for interpolation to find the net premium at the age 25 from the table given below :

    (b) By means of Lagrange’s formula, prove that approximately.

3. (a) Solve by Gauss’s elimination method the following :

    (b) Solve the following systems by Gauss Seidel method.

4. (a) Find the derivative of f(x) at x = 0.4 from the following table :

    (b) Evaluate :

     by using Weddle’s rule.

Section-B

Note : Attempt any one question.20 each

5. Evaluate:

    by Simpson’s rule, given that

    and compare it with the actual value.

6. (a) Use Newton-Raphson method to find root of the equation x² + 4 sinx = 0 correct to four places of decimals.

    (b) Find a Polynomial satisfied by (-4, 1245), (-1, 33), (0, 5), (2, 9) and (5, 1335), by the use of Newton’s interpolation formula with divided difference.

7. (a) Given with y=1 for x=0. Find approximately for x=0.1 by Euler’s method. (Five Steps).

    (b) Use Runge-Kutta method to solve the equation for x=0.2 to x=0.6 with h=0.2. Given the initially at x=0, y=0. 

8. (a) Obtain the missing terms in the following table :

    (b) Show that :

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