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Tribhuvan university > CSIT - 2065 Syllabus > Numerical Method > Old Questions > 2068
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Numerical Method 2068

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Tribhuwan University
Institute of Science and Technology
2068
Bachelor Level / Third Semester / Science
Computer Science and Information Technology ( CSC-204 )
( Numerical Method )
Full Marks: 60
Pass Marks: 24
Time: 3 hours
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.

Attempt all questions:

1. Define the types of errors in numerical calculations. Derive the formula for secant method and illustrate the method by figure. (4+4)

8 marks view

2. Define the linear least squares approximations. Give the data set (xi, yi) as (20.5, 765), (32.7, 826), (51.0, 873), (73.2, 942), (95.7, 1032) find the linear least square to fit given data. (2+6)

8 marks view

3. Evaluate  using trapezoidal rule with n=10. Also evaluate the same integral using Grossion 3 point formula and compare the result. (4+4)

8 marks view
4. Solve the following system of linear equations using Gauss-elimination method (use partial pivoting if necessary);(8)

        2x2 + x4 = 0
        2x1 + 2x2 + 3x3 + 2x4 = -2
        4x1 – 3x2 + x4 = -7
        6x1 + x2 – 6x3 – 5x4 = 6 

OR

What do you mean by eigen -value eigen- vector problems? Find the largest eigen value correct to two significant digits and corresponding eigen vectors of the following matrix using power method.(2 + 6)
        
8 marks view

5. Write an algorithm and program to solve system of linear equations using Gauss- Jordan method. (4+8)

12 marks view
6. Apply Runge-Kutta method of second order and fourth order to find an approximate value of y when x = 0.2 given that (8)

8 marks view

7. How can you solve Laplace’s equation? Explain. The steady-state two dimensional heat flow in a metal plate is defined by 

OR

A steel plate of size 30 x 30cm is given. Two adjacent sides are placed at 100°C and other side held at 0°C . Find the temperature at interior points, assuming the grid size of 10 x 10cm. (3+5)

8 marks view