Annamalai University 2010-1st Year B.Sc Computer Science 130 / 140 / 530 / 541scientific computing ( ) ( ) - Question Paper

Register Number:

Name of the Candidate :

12 6 9 B.Sc. DEGREE EXAMINATION, 2010

(COMPUTER SCIENCE)

(FIRST YEAR)

(PART-III)

(PAPER - II)

130 / 140 /530 /541. SCIENTIFIC COMPUTING

[ (Common to New and Revised Regulations) B.Sc. Information Technology (New and Revised Regulations B.C.A. - Revised Regulations) ]

May ]    [ Time : 3 Hours

Maximum : 100 Marks

Answer any FIVE questions.

All questions carry equal marks.

Register Number:

(5 x 20 = 100)

1. (a) Solve the equation

x³ + x² - 1 = 0

for the positive root by iteration method.

Turn over

(b) Find an approximate root of xlog_1Qx = 1-2. by false position method. (10 + 10)

2.    (a) Find the real positive root of

3x - cos x - 1 = 0

by Newton - Raphson method correct to

6 decimal places.

(b) By Gauss - elimination method, solve the system

315 x - 1-96 y + 3 85 z = 12 95

213 x + 512 y - 2 89 z = -8 61

5 -92 x + 3 05 y + 215 z = 6 88.

(10 + 10)

3.    (a) Evaluate

_f 71/2

0^J

1

by Simpsons rule dividing the range into six equal parts.

8. (a) Classify the equations

(i) u - 4 u + 4 u =0.

xx    xy    yy

(ii) u + u = 0.

xx yy

(b) Solve:

9 x² dy⁷

in the square mesh given u = 0 on the four boundaries dividing the square into 16 sub-squares of length 1 unit.

(5 + 15)

5.    (a) Using Taylor series method, find y(l l)

and y(12) correct to four decimal places given.

~~~ = xy^1/3 and y(l) = 1. dx

(b) Find the value of y(01) by Picards method given

= ^{Y X} and y(0) = 1. dx    y + x

(10 + 10)

6.    Apply the fourth order Runge - Kutta method to find y(01) and y(0-2) given that

y' = x + y, y(0) = 1.    (20)

7.    (a) Solve:

y , , - 2y + y = n² 2ⁿ.

^J n + 2 -'n+1 -'n

(b) Fit a curve of the form

y = ax + bx + c

for the data given below :

x: 10 20 30 40 50 60 y: 4-5 71 10 5 15 5 20-5 27-1

(b) Construct Newtons forward interpolation polynomial for the following data:

x:	4	6	8	10
y:	1	3	8	16

use it to find the value of y for x = 5.

(10 + 10)

4. (a) Using Stirlings formula, compute y₃₅, given that

yio	= 600
y20	= 512
y30	= 439
y40	= 346
y50	= 243

(b) Find a polynomial of degree four which takes the values :

x:	2	4	6	8	10
y:	0	0	1	0	0

(10 + 10)

Turn over

Attachment: annamalai-university-2010-b-sc-computer-science-16117-1.pdf

Earning:   Approval pending.