# Numerical Method | BSc.CSIT (TU) Question Paper 2070 | Third Semester

## Third Semester | Second Year | Tribhuvan University Old Question Collection | Question Bank Numerical Method, Year: 2070 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. What is bracketing and non-bracketing method? Explain with the help of example. Estimate a real root of following nonlinear equation using bisection method correct upto two significant figures.
x2 sin x + e-x = 3                                                                                                                                                                 (3+5)
2. Define interpolation. Find the functional value at x = 3.6 from the following data using forward difference table. (2+6)
 x 2 2.5 3 3.5 4 4.5 f(x) 1.43 1.03 0.76 0.6 0.48 0.39
3. Derive Simpson’s 1/3 rule to evaluate numerical integration. Using this formulae evaluate
$\int_{0.2}^{1.2} (x^2 + ln x - sin x)$dx         (take h=0.1)                                                              (4+4)
4. What is pivoting? Why is it necessary? Explain. Solve the following set of equations using Gauss elimination or Gauss Seidal method.
x1 + 10x2 + x3 = 24
10x1 + x2 + x3 = 15
x1 + x2 + 10x3 = 33                                                                                                                                                             (3+5)
5. Compare Euler’s method with Heun’s method for solving differential equation. Obtain y(1.5) from given differential equation using Runge-Kutta 4th order method.                                                                                    (4+4)
$\frac{dy}{dx}$+ 2x2y = 1 with y(1)=0                    [take h=0.25]
OR
Solve the following boundary value problem using shooting method.
$\frac{d^2 y}{ dx^2}$– 2x2y = 1, with y(0) = 1 and y(1) = 1     (take h=0.5)                                     (8)
6. Solve the equation $\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}$= 3?2? over the square domain 0≤?≤1.5 and 0≤?≤1.5 with ? = 0 on the boundary.     (take ℎ=0.5).                                (8)
7. Write an algorithm and C-program to approximate the functional value at any given x from given n no. of data using Lagrange’s interpolation.                                                                                                                                       (5+7)
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