Numerical Analysis 2019 – BSc Computer Science Part 2 (MJPRU)

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2019
Paper No. 1.3
NUMERICAL ANALYSIS

Time: Three Hours]

[Maximum Marks: 50

 

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

1. (a) By means of Lagrange’s formula, prove that:

     (b) Use Newton’s divided difference formula to find f(6) if f(3) = 24, f(5) = 120, f(8) = 504, f(9) = 720 and f(12) = 1716.

2. (a) Solve for y by Euler’s Method, up to second approximation, the differential equation

, where y = 2 when x =1 (take h = 0.5).

      (b) Find y(0.2) by Runge-Kutta method, given that:

, y (0) = 1, taking h = 0.1

3. (a) Solve by Newton-Raphson’s method, to find real root of cos x = x² in three significant figures. 

    (b) Find real cube root of 18 by Regula-Falsi method.

4. (a) Evaluate by Weddle’s rule.

    (b) Compute by Simpson’s 3/8 rule.

5. (a)Solve the following system of equations by Jacobi iteration method.

    (b) using Gauss-Seidel iteration method, solve the system of equations :

6. (a) Find y₂₅, using Newton-Gregory’s formula. Given that:

y₂₀ = 24, y₂₄ = 32, y₂₈ = 35, y₃₂ = 40

    (b) Given the following data, find f(x) as a polynomial in powers of (x-5).

x:	0	2	3	4	7	9
f(x):	4	26	58	112	466	922

7. (a) Use Runge-Kutta method to find y when x = 1.2 in steps of 0.1 given that and y(1) =1.5

    (b) Suppose 1.414 is used as an approximation to . Find the bounds on the absolute and relative errors.

8. Prove that :

    (b) Find the function u_x in powers of x^-1 given that u₀ = 8, u₁ = 11, u₄ = 68, u₅ = 123.

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