Numerical Analysis (ISS Statistics Paper I (Old Subjective Pattern)): Questions 8 - 13 of 21

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Question number: 8

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2010

Essay Question▾

Describe in Detail

If f (x) =1/x 2, find the divided differences f (a, b) and f (a, b, c).

Explanation

we can write the Newton’s divided difference formulas as

f(a,b)=f(b)f(a)ba

=1b21a2ba

=a2b2a2b2(… (205 more words) …

Question number: 9

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2014

Essay Question▾

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Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation dydx=x+y with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Explanation

The given differential equation is

dydx=x+y=f(x,y)

with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Using Euler’s method,

yn+1=yn+hf(x… (226 more words) …

Question number: 10

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Use mathematical induction to prove

fx+nh=i=0(ni)ifx

Explanation

Let ∆ i define the i th finite difference which is defined as

∆ =E-1 where E is a shift operator that is

E n f x = f x + nh

Then

fx+nh=Enfx

=(1+)n… (44 more words) …

Question number: 11

» Numerical Analysis » Numerical Integration

Appeared in Year: 2012

Essay Question▾

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The speed y (in km/hr) of a car at different points of time x between 10: 00 a. m. and 10: 40 a. m. on some day was recorded as follows:

Time x (a. m. )

10.00

10.10

10.20

10.30

10.40

Speed y (in km/hr)

24.2

35.0

41.3

42.8

39.2

Calculate the approximate distance covered by the car between 10: 00 a. m. and 10: 40 a. m. on that day using Simpson’s one-third formula for numerical integration.

Explanation

Answer: T he one-third rule of the integrand using Simpson’s rule is

abf(x)dxh3((y0+yn)+4(y1+y3++yn1)+2… (139 more words) …

Question number: 12

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

Essay Question▾

Describe in Detail

The following values of the function f (x) for values of x are given:

f (l) = 4, f (2) = 5, f (7) = 5, f (8) = 4.

Find the value of f (6) and also the value of x for which f (x) is maximum or minimum.

Explanation

This is written in the table in this function y = f (x)

x

1

2

7

8

y

4

5

5

4

For find x = 6, we use Lagrange’s interpolation polynomial because the x values is not equal interval. There are four values of x which gives the… (257 more words) …

Question number: 13

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x 2) -1 from 0 to 1.

Explanation

T he rule of the integrand using Simpson’s rule for five ordinates is

abf(x)dxh3((y0+yn)+4(y1+y3++yn1)+… (218 more words) …

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