Mohan Lal Sukhadia University (MLSU) 2001 B.Sc Computer Science Computer Oriented Numerical Methods - Question Paper

First Year exam of the 3 Year
Degree Course, 2001
(Faculty of Science)
COMPUTER SCIENCE
Third Paper
(Computer Oriented Numerical Methods)

Time - 3 Hours Maximum Marks - 50

Attempt 5 ques. in all,
choosing 1 ques. from every unit.

UNIT-I

1. How a floating point number is stored in the memory of a computer? explain with examples the procedures of 4 basic arithmetic operations using normalized floating point numbers. 10

OR

2. What do you mean by roots of an equation? explain the successive bisection method of evaluating roots of a non-linear formula in 1 variable. Develop the algorithm of the method. 10

UNIT 2

3.. explain the Gauss Seidel method for the solution of simultaneous equations. What is Pivoting? discuss its use in Gauss Seidel Method. provide a comparison of direct and iterative methods. 2+4+4

OR

4. explain the Gauss elimination method of solving simultaneous linear equations. Develop the algorithm for the method. 4+3+3

UNIT 3

5 . discuss the Euler's method of solving ordinary differential equations. Develop the algorithm of the method. explain the fault in the Euler's method. 10

OR

6. Using Runge-Kutta 4th order method obtain the solution of the subsequent ordinary differential formula at x=0.4 the intial values are y=1 at x=0. Use the steps of size 0.2. 10

dx/dy=x+y2


UNIT 4

7. What is difference table ? Construct a difference table from the subsequent data and hence using the polynomial interpolation obtain the value of function f(x) at x= 2.0 :- 10

X f (x)
-1.0 3.0
0.0 5.0
1.0 1.0
3.0 -1.0
1.0 13.0

OR

8. explain the method of approximating a function by using Chebyshev series. Use this
method to approximate the series expansion of sin (x) for 3 digits accuracy. 10

UNIT 5

9 . discuss the method of numerical differentiation. explain the fault in the differentiation formulae. Using this method obtain the differential of function f(x) at x = 1.3 from the subsequent tabulated data :- 3+2+5

X f(x)
1.0 0.0
1.2 0.365
1.4 0.673
1.6 0.940
1.8 1.176

OR

10. discuss the Simpson’s rule of numeric integration. What is the estimated fault in this method? Write the algorithm for the Simpson’s method. 10

Earning:   Approval pending.