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 :
| x | 0 | 5 | 10 | 15 | 20 | 25 |
|---|---|---|---|---|---|---|
| y | 7 | 11 | 14 | 18 | 24 | 32 |
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 :
| x | 0.1 | 0.2 | 0.3 |
|---|---|---|---|
| y | 1.105 | 1.223 | 1.355 |
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.
……..End……..
