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 :
Age | Annual New Premium |
---|---|
20 | 0.01427 |
24 | 0.01581 |
28 | 0.01772 |
32 | 0.01996 |
(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 :
x | 0.1 | 0.2 | 0.3 | 0.4 |
---|---|---|---|---|
f(x) | 1.10517 | 1.22140 | 1.34986 | 1.49182 |
(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 :
x: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
f(x): | 1 | 8 | ? | 64 | ? | 216 | 343 | 512 |
(b) Show that :
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