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 ux in powers of x-1 given that u0 = 8, u1 = 11, u4 = 68, u5 = 123.
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