Numerical Analysis 2018 – BSc Computer Science Part 2 (MJPRU)

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2018
Paper No. 1.3
NUMERICAL ANALYSIS

Time: Three Hours] [Maximum Marks: 50

Note: Attempt five questions. All questions carry equal marks. Symbols are as usual. Use of calculator is allowed.

1. (a) Evaluate :

     (b) If :

find .

2. (a) Given :

and . Find .

      (b) Find y, when x = 8 for :

3. (a) If , find the divided differences , and .

    (b) Given lof 654 = 2.8156, log 658 = 2.8182, log 659 = 2.8189 and log 661 = 2.8202. Find log 656.

4. Solve the following system by iteration method :

5. Solve the system :

by :

(i) Gauss’s elemination method

(ii) Gauss’s Jordan method

6. (a) Evaluate :

by using Simpson’s 3/8 rule.

    (b) If , prove that:

and hence find :

7. (a) Evaluate :

by Weddle’s rule.

    (b) Using Euler’s modification method to compute y for x = 0.05. Given that :

with the initial condition x₀ = 0 and y₀ = 1.

8. Solve initial value problem :

,

for x = 0.4, 0.5 by using Milne’s method when it is given :

9. Solve :

for x = 0.5 and x = 1.0 by using Runge-Kutta method, with x =0, y = 1, y’ = 0.

10. (a) Find to five places of decimal by Newton’s-Raphson method.

       (b) Compute the real root of correct to five decimal places by Regula-Falsi method.

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