# Numerical Methods || Fall 2016 || Pokhara University

 Level:  Bachelor Semester – Fall Year: 2016 Programme: BCIS Full Marks: 100 Course: Numerical Methods Pass Marks: 45 Time:  3hrs.

 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section “A”

Attempt all the questions.

10×2

1. What are the errors in numerical methods?
2. What are the bracketing and non-bracketing method?
3. What is meant by ill-conditioning?
4. Derive the Trapezoidal rule.
5. Derive the formula for Laplace and Poisson’s equation.
6. Does the following system have a unique solution or not?

X+2y=5

3x+y=5

7. Using the Picard method find the solution of dy/dx=1+xy up to second approximation where y(0)=0.
8. Derive the formula for Newton’s Divided and difference.
9. What is the initial value problem? Differentiate initial value problem and boundary value problem in brief.
10. Distinguish between ordinary and partial differential equations.
Section “B”

Attempt any six questions

6×10

11. Find the positive root of the equation corrects up to 5 decimal places using the Bisection Method.
12. Using the power method, Find the largest Eigenvalue and corresponding Eigenvector of the following matrix.
13. Fit a second-degree parabola to the following data:

 X: 1 1.5 2 2.5 3 3.5 4 Y: 1.1 1.3 1.6 2 2.7 3.4 4.1
14. The following table gives the velocity of an object at various points in time:

 Time(Seconds) 1 1.2 1.6 1.8 2.2 2.4 2.8 Velocity (m/Sec) 9 9.5 10.2 11 13.2 14.7 18.7

Find the acceleration of the object at t=2 Sec. Assume a suitable value for h.

15. Solve the following equations by using the Dolittle method.

3x+2y+z=10

2x+3y+2z=14

X+2y+3z=14

16. Use Romberg’s method to compute correct to 4 decimal places.
17. Solve initial value problem , y(0)=1 to find y(0.4) by using h=0.1.

18.

Section “C”

Case Analysis

The monthly faculty salary in three departments of an institute is given

below. Assuming that the salary for a particular category is the same in all the departments.

 Department Number of Faculty Total Salary (in thousand) Professor Asst. Professor Lecturer A 2 2 4 60 B 3 1 2 50 C 1 4 3 60

i.            Model the above problem into a system of a linear equation to determine the salary of each category of faculty.

ii.            Calculate the salary of each category of faculty

iii.            Write an algorithm to compute the above problem.

20