SPPU Numerical Method and Computer Programming - December 2016 Exam Question Paper

SPPU Electrical Engineering (Semester 4)
Numerical Method and Computer Programming
December 2016

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question fromQ.1(a,b) and Q.2(a,b)

1(a) Explain various errors with respect to numerical computation.

6 M

1(b) Explain with suitable example Descartes' Rule of Signs.

6 M

2(a) Explain various errors with respect to numerical computation.

6 M

2(b) Using Birge Vieta method, find the real root of the equation:

x^{4} - 3 x^{2} + 2 x - 7 = 0

$x^4-3x^2+2x-7=0$ / Perform two interations. Take P₀=1.3.

6 M

Solve any one question fromQ3(a,b) and Q.4(a,b)

3(a) Using N-R method, obtain the real root of the equation:

cos x - x e^{x} = 0.

$\cos x-xe^x=0.$ / Take x₀=1. Perform 4 interations.

6 M

3(b) Using Newton Backward Difference interpolation, find y at x=12, given that:

x	y
2	94.8
5	87.9
8	81.3
11	75.1
14	82.5

7 M

4(a) Explain Regula Falsi method with suitable diagram.

6 M

4(b) Fit a curve of type
y = mx + c, for the following data using Least Square approximation method.

x	y
0.2	0.447
0.4	0.632
0.6	0.775
0.8	0.894
1	1

7 M

Solve any one question fromQ5(a,b) and Q.6(a,b)

5(a) Using Gauss Jacobi interactive method, obtain solution of system of linear simultaneous equations given below. Perform 5 interations.
4x +y-z=4
2x+3y+z =4
x+ y +5z = 16.
Take x₀=y₀=z₀=0.

6 M

5(b) Using Gauss elimination method solve the following system of linear simultaneous equations:
3x-y+2z=12
x+2y+3z=11
2x-2y-z=2.

6 M

6(a) Explain Gauss-Seidel method of solution of system of linear simulataneous equations.

6 M

6(b) Using power method, find the largest eigenvalue for the following matrix:

A = [\begin{matrix} 4 & 1 1 & 3 \end{matrix}]

$A=\begin{bmatrix} 4 &1 \\ 1& 3 \end{bmatrix}$
Take [0 1] ^T. Perform 5 interations.

6 M

Solve any one question fromQ.7(a,b) and Q.8(a,b)

7(a) Evaluate:

\int_{0.2}^{1} (1 + x^{3}) d x

$\int_{0.2}^{1}\left ( 1+x^3 \right )dx$
using Simpson's (3/8) th rule with step size 0.1.

6 M

7(b) Using 4th order R-K method find y(0.1) given that:
y(0) = 1 and y'(0)=0 and

\frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} - y .

$\frac{d^2y}{dx^2}-x\frac{dy}{dx}-y.$ /
Take h = 0.1.

7 M

8(a) Find the first derivative of f(x) at x= 1.5 from the following data:

x	y
1.5	3.375
2.0	7.0
2.5	13.625
3.0	24
3.5	38.875
4.0	59

6 M

8(b) Evaluate the given integral using Trapezoidal rule. Take h = 0.2, k = 0.2

\int_{1}^{1.4} \int_{2}^{2.4} \frac{1}{x y} d x d y .

$\int_{1}^{1.4}\int_{2}^{2.4}\frac{1}{xy} dx dy.$

7 M

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