Numerical Analysis 2016 – BSc Computer Science Part 2 (MJPRU)

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2016
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 or calculator is allowed.

1. (a) Show that:

(b) Estimate the missing term in the following table:

Explain why value differs from or 27?

2. (a) Given:

Find .

(b) Use the method of separation of symbols to prove that:

3. (a) State and prove Newton-Gregory formula for forward interpolation.

(b) , find the divided differences:

f(a,b), f(a,b,c) And f(a,b,c,d) ?

4. (a) Find by using Simpson’s 1/3 and 3/8 Hence obtain the approximate value of  in each case.

(b) Find first and second derivatives of the function given below at the point x=1.2:

5. (a) Show that the expirations given below are approximations to the third derivative of .

(b) Define the following:

1. Inherent errors
2. Round-off errors
3. Truncation errors

6. (a) Solve the following system of equations by Gaussian elimination method:

(b) Find the solutions of the system:

7. Tabulate by Milne’s method the numerical solution of  with , from x=0.20 to x=0.30.

8. (a) Find the real root of the equation  correct to four places of decimals by Newton-Rap son method.

(b) Show that the square root of N=AB is given by  where .

9. (a) Determine the real root of by iteration method.

(b) Use Runge-Kutta Method to approximate y, when x=0.1 and x=0.2 and , given that x=0, y=1 and .

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