# Numerical Methods || Spring 2017 || Pokhara University

 Level:  Bachelor Semester –Spring Year: 2017 Program: 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. Define Error in numerical Process with its type.
2. State the iterative formula for bisection method to solve f(x) = 0
3. What are possible solutions to a system of linear equations?
4. Define ill-conditioned system.
5. Solve the system of linear equations using the Gauss Jordan method.

-2x – 3y = 7

3x-y = -5

6. State the iterative formula for false position method to solve f(x) = 0
7. Define the Initial value problem with an example.
8. What is the difference between the bracketing and non-bracketing method?
9. Why Gauss-Seidel method is better than Jacobi’s method?
10. Find f’(1) with h = 0.5 for f(x) = exp(x) – sinh(x) using 3-points backward difference formula.
Section “B”

Attempt any six questions

6×10

11. Using Newton’s method, find the root of the equation 3x – 1 = cos(x) such that absolute error at our calculated root should be less than 10-3
12. Solve the following set of equations by using the Crout algorithm.
13. Evaluate the integration by using 2-point and 3-point Gaussian quadrature formula.
14. Growth of bacteria (N) in a LAB after t hrs. is given by

 Time t 0 1 2 3 4 N 32 47 65 92 132

Fit a curve of the form N = bat  and estimate bacteria when t =5 hrs.

15. Solve the differential equation y’’– y+ 2x = 1at x = 0.2 using RK-2 method with y(0) = 1 and y(0) = -1.
16. Solve the PDE Txx+ Tyy= 2(x+y) over the square domain with sides     x = 0 = y ,x = 3 = y and T = 0 on the boundary and mesh length = 1.
17. Solve the differential equation  by using RK-4 method for y(0.5) with y(0) = 2 and  h = 0.25

18.

Section “C”

Case study

The monthly faculty salary in three departments of Pokhara University is given below. Assuming that the salary for a particular category is the same in all the departments, calculate the salary of each category of faculty. Use any suitable method.

 Department Number of faculty Prof.    Asst. Prof.            Lect. Total (in thousands.) IT 2             2                   4 60 Management 3             1                   2 50 Humanities 1             4                   3 60

Questions:

a)       Formulate the appropriate system of linear equations to determine the salary of each category of faculty in each month assuming that the salary for a particular category is the same in all the departments.

b)      Write an algorithm to obtain the salary of each category of faculty using the system obtained from a.

c)       Determine the salary of each category of faculty using any suitable method.

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