Numerical Analysis and Computer Programming-Numerical Integration [IAS (Admin.) Mains Mathematics]: Questions 1 - 6 of 8

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Question 1

Appeared in Year: 2016

Describe in Detail Subjective▾

For an integral , show that the two – point Gauss Quadrature rule is given by using this rule, estimate (CS Paper 2)

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Explanation

every Finite interval [a, b] can always be transformed to [-1,1] using the transformation

We consider the integral in the form

… (952 more equations) …

Question 2

Appeared in Year: 2013

Describe in Detail Subjective▾

The velocity of a train which starts from rest is given in the following table. The time is in minutes and velocity is in km/hour.

The Time is in Minutes and Velocity is in Km/Hour

Estimate approximately the total distance run in 20 minutes by using composite Simpson՚s rule. (CS Paper 2)

Edit

Explanation

If is the distance covered in t (min) , then

At, the velocity of train

The Time is in Minutes and Velocity is in Km/Hour

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Question 3

Appeared in Year: 2012

Describe in Detail Subjective▾

Solve the following system of simultaneous equations, using Gauss- Seidel Iterative method: (CS Paper 2)

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Explanation

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Question 4

Appeared in Year: 2013

Describe in Detail Subjective▾

Use Euler՚s method with step size to compute the approximate value of Correct up to five decimal place from the initial value Problem.

(CS Paper 2)

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Explanation

Here,

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Question 5

Appeared in Year: 2011

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Calculate (upto 3 places of decimal) by dividing the range into 8 equal parts by Simpson՚s rule. (CS Paper 2)

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Explanation

We have,

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Question 6

Appeared in Year: 2020

Describe in Detail Subjective▾

Find a quadrature formula

Which is exact for polynomials of highest possible degree. Then use the formula to evaluate

(Paper 2)

Edit

Explanation

Making the method exact for polynomials of degree up to 2, we obtain

For

… (149 more equations) …