# Numerical Method | BSc.CSIT (TU) Question Paper 2066 | Third Semester

## Third Semester | Second Year | Tribhuvan University Old Question Collection | Question Bank Numerical Method, Year: 2066 Computer Science and Information Technology (CSc 204) Full Marks: 60 | Pass Marks: 24 | Time: 3 hours

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

Attempt all Questions:

1. Define the fixed-point iteration method. Given the function ?(x) = x2-2x-3 = 0, rearrange the function in such a way that the iteration method converses to its roots. (2+3+3)
2. What do you mean by interpolation problem? Define divided difference table and construct the table from the following data set. (2+2+4)
 Xi 3.2 2.7 1 4.8 5.6 Fi 22 17.8 14.2 38.3 51.7

OR
Find the least squares line that fits the following data.

 x 1 2 3 4 5 6 y 5.04 8.12 10.64 13.18 16.2 20.o4

What do mean by linear least squares approximation?

3. Derive the composite formula for the trapezoidal rule with its geometrical figure. Evaluate $\int_0^1 e^{-x^2} dx$ using this rule with n = 5, upto 6 decimal places. (4+4)
4. Solve the following system of algebraic linear equations using Jacobi or Gauss-Seidel iterative method. (8)
6x1-2x2+xa=11
-2x1+7x2+2xa=5
X1+2x2-5x3=-1
5. Write an algorithm and computer program to fit a curve y=ax2+bx+c for given sets of (xi, yi, g. o = 1, …., x) values by least square method. (4+8)
6. Derive a difference equation to represent an Poisson’s equation. Solve the Poison’s equation ∇2f=2x2y2 over the square to main 0≤?≤3, 0≤?≤3 with f = 0 on the boundary and h = 1. (3+5)
7. Define ordinary differential equation of the first order. What do you mean by initial value problem? Find by Taylor’s series method, the values of y at x = 0.1 and x = 0.2 to fine places of decimal form .
$\frac{dy}{dx}$=x2y-1,            y (0)=1                            (2+6)
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