# 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:

X |
F(x) |

0 |
1 |

1 |
3 |

2 |
9 |

3 |
? |

4 |
81 |

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) ?

- (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**:

x |
y |

1 | 0 |

2 | 1 |

3 | 5 |

4 | 6 |

5 | 8 |

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

(b) Define the following:

- Inherent errors
- Round-off errors
- 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 .

……..**End**……..