Numerical Analysis 2024 – BSc Computer Science Part 2

Total No. of Questions : 8] [Total No. of Printed Pages : 4

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2024
Paper No. 1.3
NUMERICAL ANALYSIS

Time: Three Hours] [Maximum Marks: 50

Note: Attempt any five questions. All questions carry equal marks. Symbols are as usual. Use of calculator is allowed.

1. (a) Find the value of √12 correct upto 3 decimal places by Newton-Raphson method.

   (b) Find y(0,2) by Runge-Kutta method, given that : $latex \frac{\mathrm{d} y}{\mathrm{d} x} = 3x + \frac{1}{2}y, y(0) = 1, taking h = 0.1.

2. (a) Using Gauss-Scidel iteration method, solve the system of equations :

     (b) Prove that :

$latex \Delta ^{n} O^{n+1} = \frac{n(n+1)}{2} \Delta ^{n}O^{n}

3. (a) Suppose 1.732 is used as an approximation to √3. Find the bounds on the absolute and relative errors.

    (b) Evaluate $latex \int_{0}^{1} \frac{1}{1+x^{2}}dx by using Weddle’s rule, by dividing the intervals into 6 parts. Hence obtain the approximate value of π.

4. (a) Find real cube root of 24 by Regula-Falsi method.

    (b) Compute $latex \int_{0.2}^{1.4}(\sin X – \log e^{x} + e^{x})dx by Simpson’s 3/8 rule.

5. (a) Solve dy/dx = x + y with boundary conditions y = 1 at x = 0 by Euler’s method. Find approximate value of y for x = 0.1.

    (b) Find y₂₅, using Newton-Gregory’s formula.

Given that :

y₂₀ = 2t, y₂₄ = 32, y₂₈ = 35, y₃₂ = 40,

6. (a) Find y(0.4) if dy/dx = y²-x² s.t. y(0) = 1, y (0.1) = 1.11, y(0.2) = 1.25, y(0.3) = 1.42 by Milne’s method.

    (b) By means of Lagrange’s formula, find f(6) from the following table :

7. (a) Write short notes on the following :

        (i) Relative error and Absolute error.

        (ii) Percentage error and Round off error.

    (b) Use Newton’s divided formula. Find the value of f(8) from the following table :

8. (a) State and prove Newton’s Gregory formula for forward interpolation.

    (b) Solve the following equations by Gauss Elimination method :

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