Annamalai University 2008-1st Year B.Sc Computer Science " SCIENTIFIC COMPUTING " ( - II ) ( PART - III ) ( ) 6603 - Question Paper

(b) Solve

4

y' = y - x², y(0) = 1

by Picards method upto third approximation. Hence, find y(O-l).

(10 + 10)

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

y' = x + y, y(0) = 1.    (20)

7.    (a) Solve the difference equation

4y ₀ - 4y . + y = 2ⁿ + 2ⁿ.

-'n + 2 -'n+1 -'n

(b) Fit a straight line to the data given below:

x:	0	5	10	15	20	25
y:	12	15	17	22	24	30

8. (a) Classify the equations

(i)    u - 4u + 4u = 0.

xx    xy    yy

(ii)    u + u = 0.

xx yy

Name of the Candidate :

6 6 0 3

B.Sc. DEGREE EXAMINATION, 2008

(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)

December ]    [ Time : 3 Hours

Maximum : 100 Marks

Answer any FIVE questions.

All questions carry equal marks.

1. (a) Find a root of the equation x³ - 9x + 1 = 0 by bisection method.

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

2.    (a) Find the root of the equation which lies

between 0 and 1 of the equation

x³ = 6x - 4

by Newton - Raphson method.

(b) Solve the system of equation by Gauss -elimination method

3x + 4y + 5z = 18

2x - y + 8z = 13

5x - 2y + 7z = 20 (10 + 10)

3.    (a) Using Lagranges formula of interpolation,

find y(9-5) given :

x :	7	8	9	10
y :	3	1	1	9

dx

1 + x

using Simpsons rule.

4. (a) Find f'(2) from the following table :

x:	2	4	6	8	10
f(x):	105	42-7	25-3	16-7	13-0

(b) From the following table, find f( 12) by using Stirlings formula:

x:	5	10	15	20
f(x):	54-14	60-54	67-72	75-88

(10 + 10)

5. (a) Using Taylor series method, compute y(0-2) correct to 4 decimal places given that

= 1 - 2xy and y(0) = 0.

dx

3²u 3²u

+ = 0 3 x² 3 y²

in0<x<4;0<y<4,

given that

u(0, y) = 0,

u(4, y) = 8 + 2y,

x²

u(x, 0) = -,

2

u(x, 4) = x² with Ax = Ay = 1.    (5 + 15)

3²u 3²u

+ = 0

3 x² 3 y²

in0<x<4;0<y<4,

given that

u(0, y) = 0,

u(4, y) = 8 + 2y,

x²

u(x, 0) = -,

2

u(x, 4) = x² with Ax = Ay = 1.    (5 + 15)

Attachment: annamalai-university-2008-b-sc-computer-science-16214-1.pdf

Earning:   Approval pending.