# Numerical Method | BSc.CSIT (TU) Question Paper 2073 | Third Semester

## Third Semester | Second Year | Tribhuvan University Old Question Collection | Question Bank Numerical Method, Year: 2073 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. Explain the idea of the secant method to estimate the root of any equation. Using the secant method, estimate the root of the equation
x2 – 4x – 10 = 0
with the initial estimates of x1=4 and x2=2. Do these points bracket a root?                                                   (3+4+1)
2. Given the data
 x 1.2 1.3 1.4 1.5 f(x) 1.063 1.091 1.119 1.145

Calculate f(1.35) using Newton’s interpolating polynomial of order 1 through 3. Choose base points to attain good accuracy. Comment on the accuracy of results on the order of polynomial.                                           (5+3)

3. How do you find the derivative if the function values are given in a tabulated form? The distance travelled by a vehicle at the intervals of 2 minutes are given as follows. Evaluate the velocity and the acceleration of the
 Time(sec) 0 2 4 6 8 10 12 14 16 Distance(km) 0 0.25 1 2.2 4 6.5 8.5 11 13

Vehicle at time T = 5, 10, 13                                                                                                                                            (3+5)

4. What do you mean by ill-conditioned systems? Solve the following system using Dolittle L.U decomposition method.
3x1 + 2x2 + x3 = 10
2x1 + 3x2 + 2x3 = 14
x1 + 2x2 + 3x3 = 14                                                                                                                                                           (2+6)
5. Obtain y(1.5) to the following differential equation using Runge-Kutta 4th order method.
$\frac{dy}{dx}$+ 2x2y = 1, with y(1) = 0 taking h = 0.25                                                                     (8)
6. Write the finite difference formula for solving Poisson’s equation. Hence solve the Poisson equation.
2f = 3x2y
Over the domain 0≤x≤1.5 and 0≤y≤3 with f=0 on the boundary and h=0.5                                                        (1+7)
7. Write an algorithm and a C program for the secant method to find the roots of non-linear equation.           (4+8)
OR
Write an algorithm and a C program for the Simpson’s 1/3 rule to integrate a given function.                        (4+8)
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